"Also, as I recall, the British Empire was expanding at the same time. Was that also Lebensraum? "

Funnily enough it probably wasn't. Most of the Empire was acquired (at first almost accidentally) to protect trade interests. Those settlers who went out are still mostly huddling (their descendants at least) on the coasts of what were relatively empty lands. Those who went to the civilised lands went as bureaucrats and ruling castes and have been pulling out for the last 50 years leaving just some institutions and the English language.