Thanks for doing what you can to keep him inside.
As far as it being "nature"... the cat is a domesticated species...there is very little "natural" about it. And it doesn't belong in Louisiana (or is LA Los Angeles?)...it is an invasive species. I don't know about the exact stats that gsarchie posted, but I do know that cats are responsible for a lot of damage to the environment due to them being allowed to range free and hunt whatever they happen to hunt.
Oops, I almost forgot to say, I'm glad the little lizard seems to be doing better.