What Would Lucifer Do? - S3-E4
Other mistake: When Lucifer grabs Amenidiel's phone and is supposedly typing on it, he's holding it upside down. (00:06:25)
Deceptive Little Parasite - S2-E15
Continuity mistake: When Chloe and Mazikeen are at the private school checking out the other parents, Chloe is alternately holding Mazikeen's hand and not holding it between shots.
THGhostLady Parts - S2-E4
Continuity mistake: Chloe has a bruise on her left eyebrow and a cut on her right after the fight in the bar, but when she grabs Lucifer's phone the cut and bruise have swapped sides on her face, and then when she storms off they go back to their original sides. (00:30:48 - 00:31:30)
The Would-Be Prince of Darkness - S1-E3
Plot hole: During the credits, Chloe said of the victim "coroner puts her time of death between 1 and 3am", and she does indeed ask Ty's obsessive fan / ex-gf where has she been during that timeframe. When she looks at the security tape, the timecode starts rolling at 22:18 and goes on "for 3 hours." That does not account for the time of the murder at all, she has no alibi for the second half of the suspected timeframe! Not to mention, she said she saw Ty kiss the victim. When could she possibly have seen that? It's unlikely that before 10pm Ty was already drunk and getting randy with the girl, with the house full of guests. (00:25:00)
Sammo
Lucifer, Stay. Good Devil. - S1-E2
Continuity mistake: Chloe is being debriefed by her ex about the crime scene. There's a close-up of the photographer who will be the key of the case, being physically pushed away by a policeman. The scene goes on with him in the background in many shots, all on his own, snapping away as if nothing happened. (00:08:55)
Sammo Other mistake: Throughout the episode, Lucifer's car has a California license plate - but that is, just one. He is missing the one in the front. In the following episode the car does have the regular 2 plates, and when he is pulled over at the beginning (and keeps being around cops all the time), nobody raises an eyebrow at the violation of the code.
Sammo Liar, Liar, Slutty Dress on Fire - S2-E2
Revealing mistake: When the cops find the body in the hotel room, the actor playing the body is visibly breathing when he's supposed to be dead.
THGhostLucifer, Stay. Good Devil. - S1-E2
Continuity mistake: At the beginning, the preacher is walking around with the donation mug. The first kid to put a few bucks in does it across two shots and has a very notable yellow hand-held device when he puts the money in that was not there in the first shot. (00:02:00)
Sammo 
Continuity mistake: During the scene in the school corridor with Lucifer sitting down and talking to Chloe's daughter, the same extras keep doing erratic back-and-forth for no reason (for instance the girl with a white jacket and pink shoulder bag) or just plain wrong (the kid with the horizontal striped maroon sweater who walks twice past Lucifer early in the convo). (00:24:50 - 00:25:50)
Sammo The Would-Be Prince of Darkness - S1-E3
Continuity mistake: Lucifer gets waken up after his very PG foursome by Ty. When he says "Can you just help me, please?" Lucifer does not have his right hand on the shoulder of the girl, in contrast with the earlier and following take. (00:06:15)
Sammo Lucifer, Stay. Good Devil. - S1-E2
Continuity mistake: Lucifer tosses the ninja chemist doll towards the door, and it lands on the rug in front of it. Nobody picks up the doll, but when Chloe shoves him off the premises, the doll has disappeared. (00:17:00 - 00:18:10)
Sammo 
Lucifer, Stay. Good Devil. - S1-E2
Continuity mistake: The quantity of blood on the door changes between shots, incoherently, when Jimmy is hurting himself, smashing his head on it. (00:42:35)
Sammo 
The Good, the Bad, and the Crispy - S2-E18
Continuity mistake: When Lucifer is sending his mum to her new world, he is standing for the whole scene. They show a shot of Charlotte collapsed on the beach, and in the same shot, you see Lucifer on his knees in the sand. The very next shot, he is standing again. You only ever see him fallen on his knees when time starts back up again and the detectives realise where they are, which is a bit later. (00:37:25)
Quintessential Deckerstar - S3-E23
Continuity mistake: When Espinosa opens the waffle maker, initially he's holding it facing up, slightly away from him, then the shot cuts and he's holding it close to his body, facing outwards. (00:21:20)
Jon Sandys 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.
THGhost
Continuity mistake: Lucifer says that Amenadiel has a crazy theory that explains a whole list of things, but then doesn't say what the theory is. Pierce says "And you believe that?" as though it made perfect sense. But there's at least half a sentence missing. (00:02:50)
High School Poppycock - S3-E15
Continuity mistake: Lucifer is going through the blue 'Class of 3001' book, then puts down the green 'Class of 3001' book without ever lifting it up. (00:11:50)
Other mistake: When Maze is knocked down by Lucifer the second time, the footage used of her on the ground is the same footage from when she got knocked down the first time.
Bishop73Other mistake: When Julian is in custody, being interviewed by Chloe, a lawyer comes in and says a judge has released Julian on his own recognizance. Then Chloe asks what happened to the $2M bail and the lawyer says it's already been paid in full. It's one or the other, if he was released on his own recognizance, no bail would have to be paid. If the bail has been paid, he would be released and no need for a judge's order. Not to mention the fact that all of this takes place the same day he's brought to the station and hasn't had a bail hearing. He didn't even seem to have been processed, he was just being questioned.
Bishop73
Answer: As Cain theorises in the most recent 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.
Jon Sandys