Candy's spit when Lucifer ask her to marry him was improvised by Lindsey Gort (Candy). They didn't warn Tom Ellis (Lucifer).
Tom Ellis' line:
"Well, I thought since I'll never likely penetrate you, I'd commemorate the one time you penetrated me." wasn't in the script, it was improvised by Ellis.
Lauren German immediately laughed about that line that the production team haven't said "cut!"
Linda notices the signed copy of Hamlet and acts nonchalant. There are no original manuscripts of any of Shakespeare's work, not a single fragment of text. The oldest existing copies of Hamlet date to 1603 ("Bad" Quarto) and the much longer "Good" Quarto of 1604, likely to have been Shakespeare's preferred corrected version. A signed copy of either would be absolutely unique, priceless and cause global meltdowns of Shakespeare experts.
Tom Ellis has said that filming the "Luck Be A Lady" cabaret scene is one of his favorite moments of filming season 3.
Lucifer's line about Ella's lock picking skills, "Ms Lopez, you are an enigma, wrapped in a hoodie under a jaunty ponytail" is an oblique reference to Winston Churchill's quote about Russia made in a radio broadcast in October 1939, "It is a riddle, wrapped in a mystery, inside an enigma." Also a reference- most likely what they were thinking of- from The Riddler in Batman.