Lizzie was going to kill the baby, Judith, next after her sister. Lizzie was a threat to everybody. In the zombie apocalypse there was no way to contain Lizzie or give her any kind of medication. It was a horrible choice they had to be made, but they had to do it to save lives.
This show is going down scary paths, asking some scary questions, and I hope they don’t continue this kind of thinking, hoping to garner ratings.
The cannibal stuff is going to be bad enough....
This will probably be unpopular, but here goes.
I think that the writers had grown weary of the girls characters and decided to take the easy way out and kill them off before they got to Terminus. Either what is going to happen at Terminus is so socially unacceptable that they could not include them in the story, or it was decided that they were the cast members most likely not to be missed so they got the ax.
My tipoff was when the two adults travelling with them started going off on walks, leaving them by themselves. Every time they would come back, the girls were under attack by walkers. So, what did the adults do? Go on longer and more frequent walks. I got the hint.