AFAIK, Hitler motivated his belief in Lebensraum on the fact that a lot of Germans emigrated to greener pastures in the Imperial German period--something that Hitler thought could have been avoided had Germany itself had more Lebensraum. He explicitly said as much in his 1928 Second Book. Also, while Germany had relatively low birth rates (albeit apparently higher than those of Britain and France) in the 1930s, the belief might have been that if Germans would have had more Lebensraum, it would have been easier for their fertility to increase than it would have otherwise been. In other words, the logic might have been that Germans' relatively low birth rates was at least in part a result of their lack of Lebensraum--a problem that the Nazis wanted to remedy in real life by acquiring more Lebensraum for Germany and specifically for the German people/German Volk.