Continuity mistake: At the start when Trixie comes running in to give Lucifer a hug, Lucifer has got a jar in his hand. As the shot changes to him actually being hugged, the jar simply vanishes from his hand. (00:03:05)
Continuity mistake: At the beginning of the episode, a cop pulls Lucifer over. The car stops with the front wheels on white road markings. When Lucifer is shown taking off again, the street is just not the same, there's no white horizontal lines, and a manhole appears under the car. (00:02:45)
The Would-Be Prince of Darkness - S1-E3
Continuity mistake: Chloe takes the phone in Lucifer's hand as he is watching the registration. Depending on the angle Chloe has her right hand on the phone itself or off it, signaling Lucifer to stay put. (00:13:15)
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 ★