How were Manifest Destiny and Lebensraum similar?

Manifest Destiny and Lebensraum were both ideological constructs that emphasized the right of allegedly superior peoples to claim the lands of neighboring peoples they deemed inferior. Manifest Destiny in the United States referred to the supposed right of the United States to expand throughout North America all the way to the Pacific Coast. It was a very popular concept, indeed one that virtually drove the policy of the United States near the mid-nineteenth century. Supporters of manifest destiny claimed that the new century had the right to take western lands from Mexico, which controlled the entirety of the American Southwest, and of course native peoples, whose ancient claims on Western lands were not deemed legitimate. Manifest Destiny was based on assumptions that white Anglo-Saxon Americans were culturally and racially inferior to Mexicans and Native Americans, and that they thus had the right to the lands. 

Lebensraum, or "living space," was a concept formulated by Adolf Hitler. Hitler believed that Germans, as the "master race," were entitled to lands in the east inhabited by people that he deemed inferior. These included especially Russians and other Slavic peoples. Indeed, Hitler claimed that it was the destiny of the Germans to enslave these unfortunate peoples, and his invasion of Russia in 1941 was aimed in part at achieving this end. The concept of Lebensraum went a horrible step further than Manifest Destiny in that Hitler advocated, and tried to carry out, the annihilation of the Jewish people, many of whom also inhabited what he regarded as Lebensraum for the German people. Manifest Destiny was catastrophic for Indian people, but the horrific scale of the Holocaust was unparalleled in world history, much less that of the United States. But these two ideas had similar racial overtones. Hitler himself said as much when he explained his plans for the East in chilling terms. "[I]n the East," he said, "a similar process will repeat itself for a second time as in the conquest of America."