My coworker is
Elizabeth. There are two students (used to be another) who are all
Lizzie. I think there is a five year old who is always
Elizabeth, though.
I don't see
Lily or
Ella as nns for
Elizabeth.
Liza to me is the Russian nn, so I don't know how many people would use it automatically, like with
Lizzie. I think the use of nns can be situational. People seem to use them more for kids than adults, especially in the work place. Also, if someone introduces themselves one way, that's what people will call them.