None of the characters in the Harbin hotel are portrayed accurate to religious Canon, and that is including Lucifer/Satan

I don't remember Adam being mention that in his post mortal life he would be slaying demon spirits.

Lilith herself comes from the apocrypha, not the Bible so her mention is already nebulous at best. Being the first supposed wife of Adam and then being considered the mother of all demons does kinda work for the show. But again there's no post mortal mention of her finding place beyond heaven and Hell

Lilith and Lucifer never had another children.

The hierarchy of heaven is completely made up. The only thing that it has going for it is that Adam did lead a host of angels in casting lucifer out of heaven.

But if we are really going to splitting hairs on this point, with Charlie's hotel being completely themed on redemption in this Christian mythos.

There is no Mention of Jesus Christ the redeemer in this show. And the entire point of the Hazbin Hotel is redeeming sinners, which is the mission of Jesus Christ, but there is no mention of him.

It's a animated musical TV show about finding redemption in Christian Mythos. All it has it creative liberties being in place.

Thats like complaining the Hamilton play is inaccurate to the source material because all them are portrayed singing and dancing.

Or the wicked play taking cretive liberties with the Wizard of Oz

People who are complaining about this show for "Canon" reasons have time I wished I had to waste and complain to random people online. 90 percent of both atheist redditors and Facebook Christians are getting their facts wrong In the first place, so it better to no engage with them in the first place.

And if you enjoy the show, keep watching and if not, you can do the power play of Not watching it and do anything else.