I don't get why people think Lizzy was the one who killed Karen and David. We know she's got an odd view on the Walkers, but she's treated them more like pets or still "somewhat people" than anything else. It's a huge leap to go from that to savagely killing two innocent people and then burning their bodies. (Or just killing them, if we're to assume Carol is the one that burned them.)
Dude, she shot Alisha in the head! It's not much a leap at all.