It depends how much of a comparison you are looking for. In the strictest sense, which looks at the Lost Cause specifically as a movement to vindicate the righteousness of the Southern cause, there is no widespread equivalent. To be sure, in the post-war period groups such as HIAG - a veterans organization for members of the Waffen-SS - or the DRP represented a more extreme apologia, but this wasn't quite mainstream, even if they weren't entirely ostracized either.

If we look more broadly though and talk about the Lost Cause in a more general sense which looks at from the angle of providing honor in defeat, and attempting to assure the Southern soldier that even if they lost, it wasn't due to their own lack of martial ability, but rather an inevitable result of the overwhelming manpower and industrial might of the North, then certainly we can find strong parallels with the Myth of the Clean Wehrmacht. The aim here was similar, to separate the German military from the crimes of the Nazi regime, casting them as an apolitical organization which simply did their duty as German soldiers, and did so honorably, and placing the blame for the Holocaust and the multitude of war crimes upon the shoulders of the Waffen-SS and other Nazi apparatuses.

To be very clear from the start, 'myth' is used for a reason in the name, because it is complete bull, and the Wehrmacht was complicit up to the gills in the ills of the Nazi regime, but nevertheless it is a myth that held sway even in academic study of the war for quite a long time, and continues to be a common refrain in pop cultural understanding of the war. There are a few reasons for this. It was a common belief in Germany certainly, but it was also one that the Western powers were complicit in cultivating and encouraging as well for several reasons. I've written here about the lionization of Erwin Rommel, for instance, which was in large part a product of Allied praise; and I've written here about how the involvement of German veterans in the U.S. Army Historical Division's writing of works about the war in the years afterwards was ensured that a lot of early historiography, especially about the Eastern Front, influenced by uncritical acceptance of the German perspective of the war, which is exemplified by the self-serving memoirs of figured like Manstein which sought to rewrite history and remove any blame from themselves and hoist it all upon Hitler.

This wasn't only due to the Western Allies pivot to a Cold War mentality, which was giving great value to understanding the Soviet way of war, but also political concerns about allowing for West German rearmament in the 1950s, and thus the need to 'make safe' German militarism. For this, I would point to /u/commiespaceinvader's older response here which does a better job going over this angle than I could hope for.

In academic history, things have long since turned over, and you'd be hard pressed to find serious works published in the past few decades which so uncritically accept the Clean Wehrmacht as fact, but it is still something you find in lay understanding of the war. This is touched on a bit in the post linked above, but a much longer exploration can be found in The Myth of the Eastern Front: The Nazi-Soviet War in American Popular Culture by Ronald Smelser which is pretty exhaustive in its dogged coverage of the topic. In Germany specifically, things began to shift in the '80s and '90s, with two major events for the shift. In academica, it was the Historikerstreit of the late 1980s, and then in the mid-1990s the Wehrmacht Exhibition opened, which brought the debate down to the 'man on the street'. Commiespaceinvader touched on these in the context of the Goldhagen-Browning debates of the '90s which you can find here, and /u/kieslowskifan looks at the evolution of German memory here which would both provide some good coverage of the issue. It isn't something that flipped overnight though, and reevaluation continues. Rommel remains a figure honored within German military heritage, with a major base bearing his name, but you can see how things have changed over the past decade with examples such as the fighter ace Werner Mölders, who used to be similarly honored as one of the very honorable, but in the early 2000s saw his name stripped from the fighter wing in his honor due to his involvement with the infamous Condor Legion in Spain.

So that is probably the closest analogy you're going to find. There are stark differences, as while the Lost Cause sought to meld the honor of the Southern soldier with the righteousness of their cause, wipe them clean of the imputation of treason and idealize them as unbeaten martial heroes, the case in Germany was about separating the honor of the German soldier from the admitted evil of their cause so that they could be honored in spite of it. But nevertheless, they both serves not dissimilar purposes in the general sense of historical memory and the reckoning with defeat.

To return to our beginning though, there were examples which went more extreme, and I'll revisit HAIG, an abbreviation of 'Mutual Aid Community of Former Soldiers of the Waffen-SS'. Growing to some 20,000 or so members, the advocated strongly for a similar 'Clean Waffen-SS' myth to that enjoyed by the Wehrmacht. They too tried to portray themselves as apolitical, and not guilty of any war crimes - nevermind that many of their leadership, such as Kurt Meyer, had been literally convicted of them - and to portray themselves as valiant crusaders who answered the call of defending Europe from the eastern hordes of Communism, but it was a harder sell given the requirements for membership in the first place. So while HAIG was not entirely without success in its lobbying, they never established a similar 'cleanness' that the Wehrmacht enjoyed, and SS veterans were prohibited from the Wehrmacht reunions and ceremonies honoring German soldiers, and especially by the 1980s, although the German public hadn't yet reckoned with the crimes of the Wehrmacht, the Waffen-SS was fairly accepted as a scapegoat for the wartime atrocities. Internal division over whether to associate with Neo-Nazi organizations or not caused riffs within HAIG, and it collapsed in the early '90s, although local chapters would continue on without the umbrella organization.

Beyond that, there is of course also political parties like the DRP, which were attempts at a de facto successor to the Nazi Party, but my own readings focus on the military side of historical memory, so I would leave to others the political side to expand on that.

Very interesting topic and ironically one that is constantly in discussion in Germany. Disclaimer, I'm from Germany so I may not be able to provide an entirely unbiased opinion, but I try. I'll also mostly be speaking from the West German historical perspective, as after the war, you really need to discuss two entirely different narratives. I'll write a bit to the East German narrative at the end.

One of the biggest myths you will hear about German history after WW2 is that denazification was a rigorous process, frankly it could never have been. At the end of the war, about 10% of the German population had been in the Nazi party, not to mention how many people had been part of other Nazi affiliated organizations like the Hitlerjugend (Hitler Youth). Combine this with that fact that a large percentage of German lawyers, judges, doctors, professors, teachers, etc. had been Nazi Party members and you were left with a dilemna. Do you indite even the most tenuous connection to Nazism and set German societal structures back at least a few decades or do you turn a blind eye and allow for a Germany that can rebuild as fast as possible. In the context of the Cold War, Adenauer (Germany's first postwar Chancellor) and the western Allies chose te latter option. From the end of the war until about 1968, German society as a whole simply did not talk about the war. In the late 40s and 50s Germany was busy trying to rebuild, as the country had been utterly decimated, so there was little energy spared for introspection. In many ways, Germany immediately after the war returned to the pre-war consesus. What had before been the Social conservative Zentrum party became the modern Christian Democrats (CDU) and the Socialist SPD reemerged. This, combined with a capitalist, liberal, FDP party, became the post-war German consensus.

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All this changed after 1968. In that year the (West) German student movement began which questioned the post-war consensus. In the 1960s, those who had been complicit in the Nazi regime were often still alive and very often had risen to the top of society. Nuremberg had effectively decapitated German Nazism but those who had supported the party, either for pragmatic or personal reasons, were rarely punished beyond a slap on the wrist. The German student movement demanded a discussion on the topic and viewed the previous generation as complicit and focused on material gain rather than reckoning with the German past. This movement was largely socialist and left-wing and as such, combined discussions of the German past with systematic change. Now the student movement failed to turn its proposals into policy, but one thing it did do was instill a new idea into German public consciousness.

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This idea, known in German as Vergangenheitsbewältigung (The Act of overcoming one's past) has become pretty much standard since. This idea that Germany needs to atone and should feel remorse for the Second World War is in that way, somewhat new. But since then Germany has done many things, many of them symbolic to atone. The largest "concessions" (though i find the word problematic here) were in my opinion, a firm German support for Israel and renouncing any of the losses from World War 2. East Prussia, Silesia, not to mention the explusion of millions of ethnic Germans from Eastern Europe are things Germany agreed to bury in the interest of atonement. German politics sought to, in a way, reset its relations with its neighbors. By accepting the changes made to Europe and using them as baseline, Germany has attempted to rebuild its image. Those are just the actions of the German government however, the ways the populace teaches itself go deeper.

German schools have since then taught in many student's mind too much Holocaust. The newer curriculum has always stressed the harmful logic of fascism and the human suffering it has caused. So in that regard there is no revisionism being brought by the German government. It is also mandatory for German students to visit a concentration camp at some point during their schooling. That is not to suggest however, that German soceity does not have revanchist elements or those who wish to change the current consensus.

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Perhaps the most recent example of this is the AfD, Germany's populist right wing party. They have had a myriad of close calls with the far-right that have seen them lambasted by the general public and has at times brought our Constitutional Guardians (Verfassungsschutz, a sort of FBI to watch for and investigate extremist political parties so that they can ban them if necessary, one of many anti-fascist mechanisms inside the German constitution but beyond the current scope) to watch them closely. Their leading members have referred to the Holocaust as a "bird dropping on thousands of years of German history" and not been immediately expelled. This party claims that Germany has developed a sort of penance fetish, to use their words. They posit that Germany sees itself as a force of evil barely contained within a Democratic society, and that Germans should normalize nationalism and pride. That is giving them the most charitable explanation I can in an attempt to be unbiased, but if you are interested in their connections to the far-right and their, frankly almost universally accepted in Germany, anti-democratic tendencies there are a wealth of resources out there covering the rise of right-wing populism which is rightfully or wrongly covered more widely in foreign press given our history with right wing extremism.

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On the East German side, the prevailing narrative was that the regime was descended from the Communist opposition to Fascism and that all the Nazis had fled West and built the society there. Hence the official name of the German wall being Anti-Faschist Protectional Wall. This was, to be frank, utter rubbish. Plenty of ex-Nazis lived in East Germany and remained involved in state apparatuses, though of course not in very public facing roles, as this would have embarassed the communist regime. I must admit my knowledge of East German political history in this regard is somewhat lacking, so I'll recommend you a book below.

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Another chapter in this history that in many ways led to the AfD and modern populism is German reunification. The surge in nationalism after reunification had not only positive effects, as the Rostock-Lichtenhagen Riots or murder of a Turkish family in Solingen. We are also seeing a transition in German society. Those who have living memory of the Second World War are dying out and the event is frankly, fading in memory. To many a German today, the stigma attached to the country due to an event 90 years ago feels unfair. How this will develop is an interesting question, but beyond the scope of your question.

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Broadly speaking I would say there is not presently a "Lost Cause" mentality in Germany, there are people who hold such an idea, but it is not widely accepted. That may change as the war passes from living memory, but for now the memory is still too fresh for any romanticism of the conflict to happen on a massive scale.

The war remains frankly, omnipresent in German society and, speaking less as an academic and more as a German, we continuously watch ourselves and question how relationship to it. Do we respect our ancesetors who fought for Germany? Do we ever discuss the, what one could call genocide, forced expulsion of ethnic Germans from territories in Eastern Europe such as Prussia, Silesia, Sudetenland, Transylvania and the Volga? To make an easy example, VE day is widely celebrated in Europe, but in Germany it remains a day of quiet introspection. The idea that we should celebrate it as a liberation of Germany from fascism is a not-universally-accepted one and that should clue on in to the difficult questions Germany continues to ponder.

As this is getting long I'll leave it off here and link two books I consider great sources on this.

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Herf, Jeffrey. Divided Memory: The Nazi Past in the Two Germanys. 1999

somewhat old but good and applies directly to my lack of East German expertise.

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Taylor, Frederick. Exorcising Hitler: The Occupation and Denazification of Germany. 2013.

This book covers the initial denazification and does a decent job of showing the debate at the time. I caution you a tad, as the author is on the "Germany was liberated from fascism" side, which is an ongoing societal and academic discussion in Germany.

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Key Terms to guide googling if you want to know more (thought I'd try this out).

-Vergangenheitsbewältigung

-West German Student Movement

-Denazification

-Alternative für Deutschland (AfD)

-Clean Wehrmacht Myth