It's quite a leap to say that Lizzie is the one who killed Karen and David just because she treats the Walkers like pets. I mean that's a pretty damn huge leap. And I certainly doubt she has the skills to vivisect an animal.
I still buy that Carol killed Karen and David, again, she owned up up pretty easily and quickly and even seemed to have good reasons and justification on doing it.
On the vivisection and who was feeding the Walkers at the fence? I'm thinking Bob.