I like Lizzy as a nickname for Elizabeth or Lizabeth. I prefer Beth but I think Lizzy has a certain 'spunk' to it. I do like Lizzie but Jane Austen's Pride and Prejudice makes me lean towards Lizzy :)
I like the "Lizzy" spelling much better than "Lizzie". I think the "y" at the end seems to suit me better than the "ie". (My real name's Elizabeth and Lizzy is one of my nicknames.)
Lizzy Caplan bears this name, I'd believe? Well, bears this diminutive. She is an American actress, famed especially for her ever-popular outcast character of Janis Ian in "Mean Girls".