Did they know of stuff that would knock out an animal without killing it, though? And would they know how much to give–that is, the right balance between killing it and having it not be unconscious?
Trial and error, I suppose. As someone mentioned above, animal life was cheaper in ye olde days.
The answer is simple: Follow the yellow brick road.
I think if a bunch of people can run down an elephant you could probably throw enough bodies at a lion until it collapse from exhaustion then you can just tie it up with chains and leave the masses of bodies as bait for the next lion