When Ella and Lucifer meet each other Tom Ellis was not told that Aimee Garcia would hug him which means his reaction is authentic.
It really is Tom Ellis singing "All Along the Watchtower" in the piano cover that Lucifer plays at the end of the episode. However, Ellis is not a skilled enough pianist to play the song himself, so the piano part was performed by a session musician.
Lucifer makes a few (quite funny) drug references in the scene for the NA meeting. He mentioned he-she, neon nod, and a donk, which he continued to make a joke on. A he-she is heroin mixed with cocaine. A neon nod is LSD mixed with heroin. And a donk is Marijuana mixed with PCP. Furthermore, two nick names for PCP are angel dust as well as devil's dust.
First appearance of Jeremiah Birkett as the much-beleaguered Lee. Although he is named in the credits, within the show, he is addressed -if at all -by the name Lucifer thinks he introduced himself with: "Mr. Said-Out Bitch."
When Lucifer is telling Dr. Martin about the history of his family, he implies that they've only been around for a few thousand years, which is in keeping with some interpretations of Christian theology, which sees the universe as only thousands of years old, as opposed to secular science, which says it is in the billions.