Continuity mistake: When Lucifer talks to the killer in agony in the car wreck, blood streaks change on his face between shots (in particular, he has blood coming from the corner of his moith in the last shot, from the side, but he had none a moment before, in close-ups). (00:09:40)
Lucifer, Stay. Good Devil. - S1-E2
Continuity mistake: Immediately after the close-up on the poster of Demon Town with Penelope Decker, Lucifer holds the trophy. From behind it's evident that Chloe's healthy arm is down her side, but in the reverse shot she has her arms crossed. (00:17:30)

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)
Lucifer, Stay. Good Devil. - S1-E2
Continuity mistake: Talking with her daughter at the end of the episode, Chloe stifles her laughter with her hand in front of her mouth. In the matching reaction shot her hand is still on her chest. It happens again twice. (00:40:30)
Lucifer, Stay. Good Devil. - S1-E2
Continuity mistake: When Chloe asks Jimmy about Lucifer at the end of the episode, her good arm is down her side when seen from behind, or folded in the frontal views. (00:42:25)
Continuity mistake: When Charlotte is in Linda's office getting therapy, Linda is shown drawing in her notebook next to a written description of Charlotte talking to a co-worker with bad breath, before Charlotte actually tells Linda the event. (00:16:50)
The Sin Bin - S3-E10
Continuity mistake: When Chloe and Lucifer approach Maggie's car, it's parked next to a car that has pulled in forward (so the trunk is seen). But after they open the door, the car next to Maggie's car is now pulled in backwards (so the front is seen).
Stewardess Interruptus - S2-E11
Continuity mistake: When Chloe tells Lucifer that her main priority is the case and that nothing is going to happen between them, her hair on the right side of her face tucks itself behind her right ear between shots. It then falls down again, then tucks itself once more. (00:34:40)
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)
St. Lucifer - S1-E11
Revealing mistake: When Chloe is getting dressed at the start of the episode, she is wearing a flesh colored bra underneath the bed covers that she has wrapped around her when she mentions her ex dumping her by text.
Visible crew/equipment: When Lucifer jokingly says to Ricky that there's "nowhere to go but up", part of the crew/equipment is reflected in Ricky's glasses. (00:15:00)
Other mistake: When Lucifer and Chloe are talking about the Player after-party, the same extra walks by twice (in the same direction without having enough time to double back). After Lucifer says "sex afterward" and it cuts back to Chloe the women is seen and then when Chloe walks away.

Continuity mistake: When Lucifer helps Amenadiel, who has been stabbed with one of Mazikeen's daggers, Lucifer has one hand on Amenadiel and one by the dagger. The camera cuts, and now he has both hands on Amenadiel. (00:21:45)

Continuity mistake: When Linda asks Amenadiel if he is a real doctor, he has both hands raised. Camera cuts and now he only has one raised. (00:08:20)

St. Lucifer - S1-E11
Continuity mistake: The way Malcolm holds the gun when showing it to Dan changes between shots. Note his grip. (00:06:30)

St. Lucifer - S1-E11
Continuity mistake: Just after saying the widow could hold the charity event at Lux, Lucifer has his hands clasped. As the camera changes angle changes however his hands are apart. (00:07:30)
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 ★