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.

Lucifer (2015)
1 other mistake in Pilot - chronological order
Starring: Lauren German, Kevin Alejandro, Tom Ellis, Lesley-Ann Brandt
Genres: Fantasy
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)
Lucifer: Dearie me, these are atrocious. What self-respecting artist would actually display these?
Dan Espinoza: Dave Maddox isn't a real artist.
Lucifer: To say the least.
Dan: All of this is just a front. You see, criminals like Maddox, they use art sales to cover up money transfers. They can demand any price for a piece of art, and in return provide whatever it is their clients really want.
Lucifer: Can he provide an eye bath? I'll need one after this.
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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 ★