The idea of a slow song playing while the hero races to save the day was a technique used by Michael Mann on Miami Vice (1984). The same song "In the Air Tonight" was used, albeit with a different artist.
Raymond, the man Charlotte is considering buying jewelry from, also appeared in My Brother's Keeper (2018) as a sales associate at a diamond boutique strongly implied to deal in conflict diamonds and other ethically questionable practices.
David Boreanaz appears via the TV program Bones (2005), which Lucifer had been watching to avoid falling asleep. Boreanaz also played a character named "Angel" in Buffy the Vampire Slayer (1997) and Angel (1999).
The cymbal-playing chimpanzee toy Lucifer includes in his sleep procrastination campaign is a variation of the Jolly Chimp toy, which first arrived on the market in the 1950's and has undergone many variations since. Because of their unsettling nature --- screeching, teeth-baring, red-rimmed eyes, and repetitive cymbal clashing, they are often used in both horror and comedy contexts for purposes other than to give joy. They've also come to represent a disturbed, frazzled, and/or empty mind. The toy's loudness and jerky activity further handily serves to keep people from sleeping.
Lucifer says to have seen all episodes of Bones (2005). If true, would have recognized several actors who have appeared in both shows, including Aimee Garcia (who plays Ella) and Kevin Alejandro (who plays Dan).