Had a modern human AU idea a while ago.
Six year old Charlie punches Cain in the eye cause he was picking on Vaggi.
Adam makes Cain apologize and Lucifer makes Charlie apologize.
Lucifer insists on taking Adam's family out to dinner to make up for the black eye. Adam agrees because it's a chance for the kids to become friends.
From there they start being into each other.
But I like the most is the bit of backstory for them both.
Adam's a single parent because as their surrogate's (Eve's) due date grew near, his husband decided he wasn't ready to be a dad and left him. But tried to kidnap the boys when they were four because "he was ready to be a dad" but Adam wasn't letting him back into their life. The boys are biologically both Adam's and the ex took off before the boys were born so he has no legal rights to the kids.
Lucifer and Lilith are divorced, but they both knew their marriage wouldn't last (the marriage was more for tax/housing/scholarship reasons and Charlie ended up being unexpected). Lilith always wanted leave their smaller city, and follow her dreams of being a lawyer. Lucifer loves their small city, owns his own gym, and comes from a large family (oldest of seven (the sins)) and always has had enough support (financially and emotionally) to make a good life for him and Charlie even without Lilith sending child support.
So when Charlie was about to start kindergarten and Lilith was offered a job in the larger city not to far away after passing the bar exam, they got a bittersweet divorce and Lucifer and Charlie stayed behind.
Lucifer has more free time to care for Charlie, since his business is established. And she stays with Lilith every other weekend as Lilith works her way up. She and Charlie video call every night for Charlie's bedtime story, often Lilith is still at work going over files, but she stops to read Charlie her story.
I like the idea of Lilith noticing Adam and Lucifer's budding romance before they do. Lightly grilling Adam and watching him at a bbq before telling Lucifer she approves of Adam and Lucifer just fumbling out a "what?!?" Cause oh god was he that obvious???
Adam being weary because of his bad experience, but Lucifer is a great parent, Lilith isn't a crazy ex, and the in-laws seem alright.
I think the thing that would push him into giving Lucifer a chance at being more than friends, is Lilith. Lilith isn't like his ex, she's as involved as she can be while also trying to achieve her own dreams. His ex left him with only a couple months to scrabble to find child care, Adam was supposed to quit his job and care for the twins until they were old enough for preschool. Eve, his best friend and honorary aunt/godmother to the twins, helped a lot along with his parents.
In this Adam is gay and Eve is a lesbian. They have zero romantic interest and have just been best friends since childhood.
Seeing Lilith and Lucifer being friends, co-parenting even over "long-distance" (she lives an hour away) and how involved they both are for Charlie, makes him feel safe enough to trust Lucifer not to screw him over (and to know dealing with Lilith won't be a landmine).
I really like the idea that after adamsapple happens, all the kids will sometimes go to Lilith's for a fun weekend in the big city. Going to the zoo, the amusement park, the science museums. That in the distant future when she's made partner and shit that she buys a nice condo and the twins have their own room there along with Charlie. She's auntie Lil and the boys are as welcome as Charlie to come and go and crash there if they want.
(Also some Eve x Lilith in the future)