Your situation with Lizzie sounds like our Leila!
You see, Leila was sweet as could be when we met her in late April 2003, when she was up for adoption and 5 months old. We adopted her and brought her home, and then we figured out that she has two personalities - the sweet cuddly side and the devil side. She has always been that way, and it seems like that's just how she is. Leila, by the way, is a calico tabby (probably oriental shorthair of some kind) mix, and they say calicos can be a bit mean (that's putting it nicely, I think).
She goes through phases where she's all sweetness and light, unless we pet her when she doesn't want it or if we trim her claws (which is a once every couple of weeks occurrence for all of our kitties - last night was the night and it was a hoot (NOT!) as usual).
She bites us even when we think she's comfy on either of our laps and loving the attention and petting we give her. She is the bully of our four cats - she came in second, so she really scares Leo and Claudia if she wants to (sometimes she sleeps with them and plays with them calmly, and other times, she just attacks them for no reason), and probably scares Bailey when they're chasing and wrestling sometimes too, but he's the only one with "seniority" over her, so he can smack her down if needed. If she really is out of line with Leo or Claudia, we separate her from the others for a while until she calms down.
Anyway, I'm not sure if your Lizzie is just going through a phase or whatever, but she sounds a lot like our Leila, who we've come to love and accept for the crazy wild thing she is. She was on the streets alone, from what I gather, in the first few months of her life, and she's thin, acrobatic and scrappy, and probably just tough from that time. Who knows? Her father may have been an evil dude too! The fact that she snuggles with us at all (of course on her terms!) or sleeps with us practically every night is encouraging.
Good luck with your little wild child. We feel your pain! :) We both have the bite marks to prove it. :)