Downplayed: Lilith is very stern about her not believing in religion, and while she will argue her points against religion when and if it comes up, she tries not to actively seek out people to bash. "Tries" being the keyword here.
Zig Zagged: Lilith is a villain and disdainful towards religious people, whereas Isolde, though also an atheist and working for Lilith, is more understanding and eventually does a Heel-Face Turn (while she keeps her atheism).
Alice is an atheist and is an atheist simply because she finds the idea of God illogical, not because of trauma, and is friendly, happy, has a strong moral code, not hypocritical, and only argues with people if they start it.
Lilith never brings up her faith (or lack thereof).
Lilith, while villainous, doesn't appear to be motivated by lack of faith.
Lilith is a non-villainous and non-traumatized atheist.