There is nothing wrong with a cat killing a wild animal. It is called instinct. Cats are not purely indoor animals, some are, and others arent. Maybe 10 cats is excessive for your neighbor, but coming onto the forums and making a statement about hating cats because of their very nature is extremely narrowminded and ignorant.

Some animals are carnivores, and that involves killing other animals for food. Lizards may not be the primary food for cats, but neither are flies and I've seen some eat those before .

If you bring more information to bear on the situation I may rescind my comment, but unless the cat is harming your property in some way, I don't see how your neighbor is being irresponsible. A cat walking across your property isn't hurting anything, but if it is peeing or pooping or killing your pets or harrassing your dog or something, I can see it becoming an issue.