Tell us your headcanons/theories.
For me I believe Lilith is nothing like how Charlie says and thinks she is, in fact Lilith hates Sinners just as much as Lucifer. Afterall why should she like them, they are the spawn of Adam and her replacement who got to populate earth with their descendants, while she was cursed to not have kids until Charlie was born.
The whole inspiring them to rise up was actually her way of getting the Exterminations to happen, because she wanted to make Lucifer happy by having sinners slaughtered since he couldn't do it himself.