> The lion kills and hunts to eat, but the lion doesn't kill the entire living creatures in Serengeti or elsewhere to later die himself from hunger.

I don't know about lions, but their cousins the lynx absolutely do kill off so many hares that they die of hunger. The hare population then rebounds, followed by a rebound in the lynx population. It's one of the most famous cycles in ecology.

I would not be at all surprised to learn that a similar predator/prey population cycle holds true for lions.

https://www.enr.gov.nt.ca/en/services/lynx/lynx-snowshoe-har...

If you're interested in the math:

https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equatio...