Basically, Lizzie went crazy, and she’s been crazy for quite a while. Lizzie was the one feeding rats to the walkers at the chain link fence at the prison, which was attracting more and more walkers to the prison. She was the one who had been dissecting rats at the prison (Tyreese found one). Lizzie killed the little bunnies while they were in the woods. She thought that the walkers were just misunderstood.
After Lizzie killed her sister (Mika), Carol realized that she was too dangerous to keep around - especially around baby Judith. In a normal world, they would have locked Lizzie up and gotten her medical treatment. But, this is the zombie apocalypse, so they didn’t have much other option than to get rid of her because she was a threat.
The actress who played Lizzie did an excellent job. She’ll go far.
Feeding rats to walkers is crazy but it wouldn't attract any others. It's not like they can call out to each other and say "Hey, someone opened up a rat restaurant down here!" The mere fact that anyone was there at all would be what attracted the first ones, then the noise would attract others. Walkers don't have enough intelligence to hang around waiting for treats.
One thing I do wonder is why the walkers have to eat at all since so far I haven't seen any evidence that they starve to death if they don't. It seems more like they are driven to murder rather than to eat and their teeth are their only weapons. But that doesn't explain why they hang around to eat their victims once they are dead. I guess some questions are better left unanswered so the show can go on.
YES! Exactly, I forgot about that! The dissected rat nailed to the wall! She was a freakin’ nut. Thanks, now I get it.