Chloe mentions how the murderer in a case was the first person with whom they spoke, and both Lucifer and Chloe seemed shocked by this. This is a satirical call-out to the fact that most murderers in this show are the first person to whom the detectives talk.
The title of the episode is an allusion to Season 1 of Heroes (2006): "Save the cheerleader, save the world."
Maze says to Dan that she didn't traipse over to "be your Whoopi Goldberg"; this is a reference to Ghost (1990), in which Goldberg was a medium who could see and converse with Patrick Swayze, who had been murdered and was a ghost.