[Nadya]

We could kill off nearly every other species on the planet, including many of which we have domesticated and breed for product (bees, cows, etc.) and humans would be just fine.

The only sad thing about a species going extinct is it is one less species for us to study and learn from. It's a drastic loss for science and the only hypothetical loss for people at large is if there was something of value lost (e.g. discovery of a gene that cures a disease that only the now-extinct animal naturally produced)

You can especially kill off most apex predators without issue. Which is why the loss of a lion isn't a big deal.

Now if all producers were to go extinct and the bottom feeders of the food chain(s) such as plankton were to vanish from the Earth? Most, if not all, life as we know it would die from starvation. The animals with the most adaptive and most abundant food sources would live the longest, but eventually they would also run out of food!

A lion isn't a producer nor is it the bottom of the food chain. So a lion dying or lions going extinct really doesn't matter outside of scientific studies.