Myths do have power, though not over everybody, and it's only sensible to consider this.
Lilith is a pretty familiar character - I'm neither Jewish nor Catholic (atheist in fact) and I know the story well. It's out there.
I dislike
Lily and all the similar names -
Lilith,
Lilian - going around. So it's not an issue for me. I find
Delilah and
Jezebel excessively biblical, apart from their unpleasant personalities: once again, no problem.