living space vs lebensraum

living space and lebensraum both are nouns.

Word	Noun	Adjective	Verb	Adverb
living space	Yes	No	No	No
lebensraum	Yes	No	No	No

As nouns, living space and lebensraum are synonyms defined as:

living space and lebensraum: space sought for occupation by a nation whose population is expanding

living space (noun)	lebensraum (noun)
space sought for occupation by a nation whose population is expanding	space sought for occupation by a nation whose population is expanding