Continuity mistake: At the start, the man's hands change position around the woman during instant cuts. (00:01:40)
Character mistake: When trying to decipher what the letters from the dermal implants spell, Lucifer rearranges the letters and says "Hilii Fircus, it means 'children of the goat.'" However, the correct phrase was Filii Hircus, not Hilii Fircus. (00:13:27)
Continuity mistake: When Onyx opens the box, the way he holds the lid changes between shots. (00:19:50)
Continuity mistake: In the scene in the warehouse, Chloe and Lucifer end up right below where Corazon is tied up. Then blood drips on her hand prompting her to look directly above her head. In the next shot Lucifer turns around and suddenly they're both meters away, looking at the contraption from a distance. (00:26:50)
Continuity mistake: When Chloe turns the picture of the cufflink upside down to Dan, her grip on the photo changes between shots. In one, she has one finger behind the picture, but in the front angle, all of them are at the front. (00:33:10)
Answer: As Cain theorises in a later episode, it's Chloe's love, not presence. This early on, Chloe had no strong feelings for Lucifer, so had no effect on his immortality. In fact even more recently he's back to being invulnerable around her after speculation that he chose to let himself be vulnerable. So while there's a degree of flexibility / retconning going on, it's all explained in-show.
Jon Sandys ★