> The extinction of most of their prey likely did the lions in

Maybe, but the opposite situation is also possible. You can wipe the preys if you remove the predadors. We had see this in New Zealand for example where Tasman devil has protected decens of species of smaller marsupials, extinct in the continent but not here. This is the same big scale experiment that we are playing currently in Africa. In one or other case the result is the same, almost all european big mammal fauna vanished; and a replace is still missing for the equivalent of european elephant, european rhinos or north american cheetah.