Aimee Garcia (Ella) said she had trouble keeping a straight face during the hostage scenes because Tom Ellis kept making her laugh.
Tom Ellis (Lucifer) spent three days sitting in a pool of fake blood for the hostage scene, long enough to acquire a blister in a sensitive area.
Lucifer facetiously acknowledges that "their" suspect chases involve Chloe doing the chasing while he watches. This is the first time this aspect of his character is directly noted within the show. He is seen full out running after a suspect only once - in the alternate universe episode Once Upon a Time (2018), which is outside of show canon. Otherwise, if he chooses to go after a suspect himself, his methods are more often in the "quietly menacing" category: advancing slowly and meaningly, breaking into their places and lurking at leisure in the shadows until they turn up, or moving at such supernatural speed human eyes can't follow.
The red vintage car that Lucifer drives in this episode is a 1963 Aston Martin DB4. Only 70 cars were made.
A.V. Club reviewer LaToya Ferguson gleefully noted that the title is a synonym for "Die Hard." She appears to be the first, possibly only, early reviewer to have spotted the wordplay.