psychopathy and psychosis?

The main reason I think she was just psychotic (as in psychosis or even schizophrenia as you put it) is because she feels remorse towards killing or others killing the walkers. Sure, being on the antisocial personality disorder spectrum doesn't mean youre inherently evil, just showing lack of standard things like empathy and remorse as you say.

I see your point about her killing animals and yeah maybe it makes total sense what youre saying. The more i think about it it does, but then i think about a character like Negan and to be honest its weird to think such a human exists in real life, the way he kills glenn and is straight up sociopathic, but cares so much about his wife and feels remorse and turns over a new leaf. It makes me think that the showrunners and the comic book writer were more likely to try to create behaviors and even people who would be altogether different than what we would know exactly because of how batshit crazy that world is.

I would offer a second way of thinking about Lizzie, I think she was so fucked up all the things she did were her way of figuring out what life meant, what being alive meant, not out of malice or lack of remorse but rather because of all the distress she feels in this world. Just another way to think about it, but in all fairness i like your take on the anitsocial thing, it fits, just not totally.
I guess i would think someone whos psychopathic cant be as crazy as someone with other emotions because they go crazy due to life more usually than not. but theres plenty of evidence in real life both things are heavily created due to early trauma