When the psychic talks about how she was working with a person who works in TV, specifically at Fox, Lucifer says, "good luck with that", clearly a dig at the Fox network for canceling Lucifer.
Trixie and Dan are playing a real-world game called Unstable Unicorns in which the most colorfully dressed player really does go first.
Dan hearing about Amenadiel's new job and sarcastically saying that an angel and a detective working together makes perfect sense, is clearly a dig at the show.
Rob Benedict plays Vincent. He previously played God/Chuck in Supernatural (2005). In this series, God is played by Dennis Haysbert.