When Lucifer sings "Crime-solving Devil, it makes sense, don't overthink it," he is singing to the tune of the show's theme song, "Being Evil Has a Price," by the band Heavy Young Heathens.
The Heavy Woolies are named after the former, real L.A. band for which co-showrunner Ildy Modrovich was lead singer.
Anthony Annan says that Ash's death was "the night the music died." On Feb. 3, 1959 three of rock-and-roll's early stars, Buddy Holly, Ritchie Valens, and The Big Bopper Richardson, died in a plane crash. The 1971 song "American Pie" called that event "the day the music died," and the name stuck.
In the scene of Charlotte telling Lucifer about the Flaming sword that could bring them home, there are pomegranate paintings hanging on the walls behind them. In the ancient Greek myth about Hades and Persephone, Hades feeds pomegranate seeds to Persephone before letting her go, this way making sure she would return to the Underworld.