At the time, the area Hitler demanded from Lithuania may have been seen as within Hitler's original demands and within Germany's rights. That was territory that had been detached directly from the German Empire after the first war, much like the Sudetenland. There was a four power agreement to protect the status quo, but two of the four powers were already Germany's allies (Japan and Italy) and France and Britain were still trying to prevent war.

In addition, Lithuania's own claim to the Klapeida was founded on a mutual agreement between Germany and Lithuania, one that Hitler by that point may have dismissed; the status quo itself had come into being by a refusal of the western powers to risk war with the soviets by forcing Lithuania to return it to neutral control.

People did worry that by retaking that area of Eastern Prussia, the next German move would be an attack on Poland to secure the Danzig and its corridor, but the French (and to a lesser extent the British) did not at the time have the morale for a forceful response. Perhaps had the Soviets acted more vocally dynamics would have been different, but the evidence seems to suggest that Moscow was more focused on their negotiations with Berlin and given a choice between the two there's no real reason to believe Vilnius would have picked Stalin over Hitler.

Postwar, the relations between Germany and the Baltic states probably didn't get much study for the simple reason that they de facto ceased to exist. They were not Warsaw Pact members, they were instead essentially incorporated into the Soviet Union. Soviet policy for many years was to paint the old Lithuanian government almost as aggressors and certainly as collaborators with the Nazis.

English histories about the region in the interwar years are few and far afield. I believe there was some university press book about the Baltic and the outbreak of the war, but I can't recall its proper name I'm afraid. Cambridge university, I think.

My go to popular source for WW2 is Robert Leckie's Delivered from Evil, though I don't think he gave your question more than a paragraph or two. There was an excellent book about interwar diplomacy that I had to read at school, but it's been a very long time. The Twenty Years Crisis, or something of that nature.