They're not faithful at all. The names are there for a few of them (Lucifer and Mazikeen), and there's some other references (action taking place at Lucifer's club called The Lux), but other than that? No similarities.
seasons 1-3 Fox, seasons 4-6 netflix
A Lucifer soundtrack, including scene descriptions, can be found on Tunefind. There are also user created playlists on Spotify and an official album on all popular music streaming services.
The FAQ items below may give away important plot points.
Related lists from IMDb users