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.
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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.
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