Mika was a perfectly innocent, normal, little child. She reminded me a lot of my niece and a couple of the kids in my mom's daycare.
Lizzie, it's likely she suffered from some kind of mental issues that she was getting treatment for pre-ZA. After the apocalypse obviously those treatments, and more importantly medications, were no longer available so she receded back into what ever condition she had. That or she was just in a very, very extreme state of denial.
I watched the episode last-night with a friend and he liked it too and was shocked when Mika got killed and then when Carol killed Lizzie. But he agreed there wasn't much that could be done considering Lizzie could never be trusted around on with anyone ever again since she was obviously "crazy" on some level beyond which they had the ability to deal with.
It was not an easy situation and it's not like they made the "right" choice but, really, there was no "right" choice in that situation. Watching it again it still emotionally hit me just the way Lizzie was freaking out at the end and upset and then... ugh.
But a great episode.