Quoting Dr. Carroll P. Kakel’s The Holocaust as Colonial Genocide: Hitler’s ‘Indian Wars’ in the ‘Wild East’, pages 12–6:

Lebensraum became an important element of Wilhelmine politics largely due to the work, ideas and influence of Friedrich Ratzel (1844–1904). A well‐known geographer, writing at a time of German imperial growth and conquest in Africa, Ratzel invented the term ‘Lebensraum’ in the context of his own biological theories (or what he called ‘bio‐geography’).

He was one of the founders of the Pan‐German League, was instrumental in formulating the demand that Germany acquire new ‘living space’ (or, as he liked to put it ‘elbow room’), and was a leading pre‐World War I advocate of Lebensraum imperialism.

In his 1901 book, Lebensraum, Ratzel [mis]applied the Darwinian struggle for existence to humans, expressly noting the extermination of the American Indians and other ‘less civilized’ peoples by Euro‐American conquerors. Rather than projects of trade or exploitation of ‘native’ labour, he favoured settler colonization as the most effective way to find new ‘living space’ for an expanding population, as well as wars of conquest, which ‘quickly and completely displace the inhabitants, for which North America, southern Brazil, Tasmania, and New Zealand provide the best examples’.¹⁵

[…]

While admitting (and regretting) that it was too late for a German colony in an already‐settled North America, he favoured southwest Africa as a site of German colonization. Ratzel’s thinking was also influenced by an American‐inspired romantic, peasant‐oriented agrarianism; his notion of ‘colonization’ called for the conquerors of new ‘living space’ to ‘obtain’ agricultural lands from the indigenous inhabitants for direct, small‐scale farming by the settler occupiers.¹⁸

Like many late nineteenth‐ and early twentieth‐century intellectuals, Ratzel did not develop or evolve his ideas in isolation. At the turn of the twentieth century, in fact, he was part of a growing transatlantic dialogue between politics and geography — a dialogue that included the American historian Frederick Jackson Turner.

For his part, Ratzel had complimentary things to say about Turner’s recently formulated ‘frontier thesis’ of American history, a thesis which celebrated the irresistible march of ‘white’ Anglo‐Saxon civilization across the North American continent, the ‘colonization’ of America’s ‘Great West’, and the ‘frontier’ as the incubator for ‘Americanness’.

[…]

Widespread early‐ and mid‐twentieth century German support for Lebensraum imperialism was principally due to the work, ideas and influence of Karl Haushofer (1869–1946), a student of Ratzel and a geography professor at Munich Polytechnical University (where his father, Max, had been a colleague of Ratzel’s).

A retired Bavarian general, World War I veteran, and holder of a doctorate, Haushofer — building on Ratzel’s ideas, work and arguments — reconfigured Ratzel’s ideas about geography and political history into a new formalized system of political thought, called ‘geopolitics’.

As the prophet of the new ‘geopolitics’, Haushofer envisaged the new discipline as the study of Raum (space) for the German nation‐state. ‘Geopolitics wants to be, and must be,’ he wrote, ‘the geographic conscience of the state.’²⁴ In the 1920s and 1930s, Haushofer became the foremost German geopolitician of the Weimar (1918–1933) and Nazi (1933–1945) eras.

[…]

At the University of Munich, one of Haushofer’s devoted students was Rudolf Hess, an early convert to the fledgling [NSDAP] and party leader Adolf Hitler’s private secretary. Through Hess, Haushofer was introduced to Hitler. In 1924, Haushofer visited Hitler and Hess in Landsberg Prison (where the [NSDAP’s] leaders were serving time for their part in the failed Beer Hall Putsch of November 1923, a [Fascist] attempt to topple the pre[fascist], [pseudo]democratic Weimar Republic).

Haushofer visited Hitler and Hess numerous times to ‘educate’ them (Haushofer’s word) in the theories of geopolitics and Lebensraum. Privately, via Hess, he fed the [Fascist] leader his ideas about ‘living space’ and ‘just wars’ of expansion and conquest. In turn, not surprisingly, many of Haushofer’s ideas found their way into a new book titled Mein Kampf (My Struggle) which Hitler was dictating to Hess during their Landsberg incarceration.

Dr. Kakel’s The American West and the Nazi East: A Comparative and Interpretive Perspective, page 35:

Hitler was fascinated by what a recent historian has termed ‘the North American precedent’, and he was captivated by its ‘Nordic’ settler pioneers who drove Early American westward expansion.⁷⁹ For the future [Fascist] Führer and leader of the [Third Reich], the ‘Nordics’ of North America, who had ruthlessly pushed aside the ‘inferior’ Indian ‘race’ to secure new land and soil, would be the model for future German expansion.

If pushing westward in North America at the expense of ‘native’ indigenous peoples had been necessary for the ‘Nordic’ Americans, Hitler reasoned, it was equally ‘logical’ for German settlers to acquire ‘space’ for themselves at the expense of indigenous Slavs and Jews in order to create their own Lebensraum in ‘the East’.

Before and during the Third Reich, the mystique of the American ‘frontier’ would become an addiction among many other [Fascist] ‘true believers’. In their view, the eastern Lebensraum would be to Germany what the ‘frontier’ was to America: the foundation of future global power.⁸⁰

(Emphasis added in all cases.)