I like both
Lillian and
Evelyn. I prefer
Evelyn without a nickname, but I don't mind
Evie. I like the nickname Ev more. It sounds more like
Evelyn, and I just think it sounds better.
I know of someone with a neighbor named
Evelyn who is around 8. He referred to her as
Evelyn, so I'm assuming that she is usually or always called
Evelyn rather than
Evie or another nickname.
My guess is that a lot of girls named
Lillian are called
Lillie, but girls named
Evelyn seem more likely to be called by their full names.