Well, it's up to you. If you really love it, go ahead and use it, in time it will come to mean "my daughter" to you rather than "night sorcress, demoness, etc." If the meaning on the other hand overrides your love of the name, then you might have to give it up.
Lily could be an alternative then, at least it's assonant to
Lilith.
Personally, I'm not bothered by the religious implications since I'm not religious, but it's not a name I'd use it, it's interesting but a bit burdensome.