Since we first met lizzie, it was clear of her stance that she didn't understand what the zombies were. She was giving them names and feeding them. And it wasn't just this episode that clearly showed her problems, she started suffocating Judith and killed rabbits for no reason before this episode.
Mental illness cant be dealt with the same way it is in our society. There is no place to send them to "feel" better. You either get with reality or be dealt with the same way a criminal would be. They are just as dangerous if not more.
It was still shocking as Hell when we realize that she brutally stabbed her own sister.