Unfortunately, along with the name
Seth (Egyptian God of Evil), I would never even consider using
Lilith. I wouldn't wittingly use a name with any 'evil' connotation... you know, "just in case."
I named my son
Claude despite it's meaning, because although it wasn't a 'good' meaning, it wasn't nasty.
I would suggest you use
Lillian, or
Liliana maybe, I would suggest
Tanith, but again that has a not so nice side.