I was reading an article about the sociological roots of fascism (it will be all Greek to you) and it mentions in passing that "the Nazi empire took the model of British imperialism and applied it to the European continent, treating Europeans like colonialists treated the Africans". It cites Mark Mazower's Dark Continent: Europe's 20th Century to back this up.
Now, my understanding is (and correct me if I'm wrong) that
The concept of Lebensraum is loosely related to colonialism.
That racist ideas of cultural/genetic superiority pre-date the Nazis and that Nazi Germany's implementation and rhetoric had a lot of mainstream support in other countries (until the end of WW2, when the trend was reversed).
The question is: From the above, can we conclude that the narrative of "the superior Aryan race that deserves to expand" etc borrows heavily and directly from an equivalent similar narrative of superiority that, say, the British used to justify their colonialism?
I wouldn't lump all fascist movements together to make a monolithic claim about the influence of colonialism; fascism (as a broad ideological movement) arose in early 20th century Europe as a result of the social, philosophical and cultural impacts of industrialisation, tensions between the bourgeoisie, organized working class and the traditional political elite, the impact of the Great War and general feelings towards ideas like masculinity that are hard to quantify.
It is important to remember that because fascism was based around the idea of national renewal, each national brand of fascism had different goals and perspectives inherited from the political and social discourse of its respective country. So while German fascism (Nazism) was concerned with biological race and territorial expansion, fascism in Ireland was mostly concerned with clerical anti-Semitism and the political and economic order of the newly independent Irish Free State.
Because of this, we have to look at what sort of political, economic etc. ideas were important in each country immediately before the rise of fascism. In Germany, ideas about the supremacy of the German race (defined biologically), anti-Semitism, anti-socialism and liberalism, the establishment of a corporatist state and eastwards expansion had been popularly consumed since the late 19th century, with the popularization of the works of Ernst Haeckel and the general political atmosphere of Willheline Germany. The Nazis didn't necessarily invent any of these ideas, they simply adopted them because they were a primary concern of the German educated public, especially in the middle class. Eastward expansion was proposed by individuals like Haeckel because they felt that something had to be done to stem the mass immigration of Germans to the Americas.
The idea of a German militarily and economically dominated 'Mitteleuropa' had been a war goal of the German Empire had they won the First World War, and it is possible that grain requisitioning and the establishment of a colonial 'Ober Ost' in the occupied Russian Empire gave the German political and military elite thoughts about the necessity of eastwards expansion to stem future British blockades and relieve their dependence on raw materials provided by the British Empire. Under the Nazis, these notions of eastwards expansion were combined with the perceived necessity to eradicate 'Judeo-Bolshevism'.
While the German idea of eastward expansion definitely drew inspiration from imperial rhetoric, its Nazi incarnation was more inspired by American and Canadian expansion westwards. Hitler drew explicit comparisons between the Slavs whose land was to be taken for German colonization and the 'Red Indians' of the Americas, and wanted to create an autarkic internal economy which he believed existed in the USA. In one table talk on the 17th of October, 1941 Hitler told his subordinates to "look upon the natives as Redskins" and addressed any moral qualms with taking Slavic land for German economic exploitation by saying:
I don't see why a German who eats a piece of bread should torment himself with the idea that the soil that produces this bread has been won by the sword. When we eat wheat from Canada, we don't think about the despoiled Indians.
Fascism in Italy was much more influenced by more 'traditional' imperial expansion, being concerned more with the prestige of establishing an empire than the creation of an autarkic imperial economy. Unlike Hitler, Mussolini vehemently denounced the existence of biological race, saying that "race: it is a feeling, not a reality; 95% a feeling". Italy did adopt racial laws later on, but it was arguably more of an attempt to jump start the stagnating fascist movement than a sincere attempt to create a racial utopia.
In his excellent book, The Anatomy of Fascism (New York, 2004), Robert Paxton reminds us that there are some key differences between nazism and fascism. At the crux of his argument is the idea that most scholars attempt to define fascism by using Nazi Germany as a case study. This method, he claims, is specious at best. Instead, he sets out to identify the key points that constitute fascism across European and North American lines. In the end, Paxton comes up with a number of ideas that he believes answer the question- what is fascism? (Paxton, p.219) I think they are useful in addressing your question:
In this way, some of Paxton's points highlight a few similarities between fascism as an ideational force and colonialism (whether British or otherwise). However, whether National Socialism in Germany borrowed directly from Britain's colonial policy remains debatable. Comparisons of this nature can be very problematic, too. For example, National Socialism in its varying hues and colours adopted a rhetoric of the "chosen people" that required expansion at the expense of another people. Does this mean that certain fascisms were influenced by or borrowed either directly or indirectly from Zionism? If fascism exists today, it tends to be under the auspices of confessionalism. In other words, "religious fascism" remains with us.
While I can't read the article, based on your summary I would say that it is a little off base. What you are talking about is called Sonderweg or the Special Path that some historians think Germany took in the 18th century that lead to the rise of the Nazi party. It's a bit of a dead horse at this point, but some modern historians don't have a lot of faith in it.
The narrative has changed from England, Spain and France being the default or normal model for all colonial nations and modernization, to an understanding that each country has taken it's own path towards modernity. Sometimes they are similar, sometimes different, but each is fairly unique. So to call Germany's path different or special somehow is seen as a way to isolate Nazism and pretend that fascism cannot arise in other countries.
Defining a normal for colonialism is difficult because it happened so different at different times and places. There are common themes, but colonies that were right next to each other were often managed vastly differently. Many people tend to forget the Herero and Namaqua genocides that were carried out by the Germans in 1904 and 1907, respectively. They saw concentration camps, familiar rhetoric, mass executions, and ethnic cleansing that would not seem out of place 40 years later. At the same time and not so far away the Rehoboth Basters were given nearly total self governance. Samoa and Chinese colonies run by the Germans also saw far better treatment than many.
Despite some colonies receiving 'good treatment', Steinmetz, in The Devil's Handwriting is quick to point out that generally German treatment of natives in Africa was not so different than “... colonial massacres by Spain and the United States in the Americas, the British in Tasmania and Kenya, the Belgians in the Congo, the Italians in Libya, and the French in Madagascar and Algeria...” Good treatment of a colony is still brutal and destructive.
So, all that said, is Lebensraum a form of colonialism? I think that depends on if you think German colonialism was so different than other great powers attempts at colonialism. I think most people would agree it has it's basis in it, and it is loosely related. Where did the Nazi ideals come from though? Clearly they were not born from Hitler's head fully developed like Athena fully armed for war. They slowly developed over centuries and were radicalized with the rise of the Nazi power. It is a tough balancing act putting an appropriate amount of blame on Hitler and the Nazi's while not denying the German people their agency.
Does Nazi expansion doctrine borrow heavily from British colonial doctrine? I would strongly say no, with the caveat that there is always some bleeding over among European powers. The German people had plenty of their own experiences in colonialism without needing to steal someone else's notes. While the British felt there was some inherent superiority to the British people it never went so far as to purposely eradicate whole peoples. This sort of feeling was not uncommon anywhere. The British felt they were superior to the Germans and French. Certainly large numbers of people died under the British watch in India, China, Ireland, and so on, but there was no driving doctrine of racial superiority behind the killings. It was almost always a matter of economics (including poor planning), warfare, or just plain indifference.
For further reading I would recommend:
The Kaiser’s Holocaust, Germany’s Forgotten Genocide. This book isn't quite scholarly, but is a recent and great book written by Africans from their perspective on colonialism.
Absolute Destruction: Military culture and the practices of war in Imperial Germany Hull's classic on the rise of militarism and it's origins in German colonies.
The Devil’s Handwriting, Precoloniality and the German Colonial State in Qingadao, Samoa, and Southwest Africa Provides a good overview of three very different colonies managed by Imperial Germany
Colonial Fantasies. Conquest, Family, and Nation in Precolonial Germany, 1770-1870 An excellent look into the mentality among Germans leading up to their colonial adventures.
This comparison is apples and oranges. Fascism/Nazism were ideologies; colonialism is a form of occupation or extra-systemic governance. The fact that both involved imperialism tells us no more than the fact that both involved soldiers.
Colonialism is not an ideology; its a form of occupation. Also, discussing "European" colonialism would be problematic, there were many forms and functions of colonialism between the British, French, Spanish, Portuguese (etc.) variants.
The two have no direct relationship; jut because one came first and both potentially (bot not necessarily) involve racial superiority, does not mean they are related. At best you could say that Nazism wanted to duplicate British success, but this would be bad causal logic and would be historically inacurate (Niall Ferguson documents Hitler's opinions of British imperialism pretty well in Empire).
The British narrative was not based in racial arguments, but instead with liberal capitalist ones (again, see Ferguson). That doesn't mean there was no racism involved. The jewel in the crown of British imperialism was India; there were never any plans for the British to use India as a 'lebensraum' or to evict or massacre Indian people. The goals of the British empire were liberal capitalist.
I'd say asserting a connection between British imperialism and Nazism is not only inaccurate (and anachronistic), its bad history, and weak causal logic.