What about sticking with Tiger Lily, which I think is a really nice name.
Do you have any particular interests, films, music etc?
I've used:-
Etta Place -the Sun Dance Kid's girlfriend, I like the film with Paul Newman a lot
Goodge Street - An Underground Station, I just liked the sound of it
Hera - a Greek Goddess, I'm intersted in the greek myths
Holy Cow - because she was a right old cow!
A friend had The Mean Fiddler after a music venue she went to.
So I'd be temped to use a film or music that you like for inspiration.