Everything's Coming Up Lucifer - S2-E1
Lucifer Morningstar: Hello. My name is Lucifer Morningstar, and I love drugs! Love them. Mmm. Yummy, yummy, yummy. Can't get enough. And I've got lots of money. [Pulls out cash and sniffs it.] Mmmm! That I love spending on drugs.
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 ★