Overpopulation was not the issue. The idea of lebensraum wasn't so much extra physical space for people to live in, but good agricultural land to support a larger class of German peasant farmers. The idea is fundamentally rooted in contemporary conservative ideas about the need of the German people to return to their farming peasant roots instead of urban industry, although not all Nazis shared these views or interpreted them identically. The idea also had larger economic meaning- a key part of Hitler's ideology was the idea that the Germanic people needed to command a large continental economic bloc to resist the growing influence of the Anglosphere, particularly America, which he saw as a liberal democratic puppet state of 'world Jewry'. So, yes, when interpreted through the lens of Nazi ideology, there was a 'need' for lebensraum but the need is largely based on economic realities resultant from Nazi policy. Source: Adam Tooze's The Wages of Destruction, will source with page numbers/specific passages upon request (don't have my copy super handy right now).