Huh, this is interesting because the dynamic between Lilith and Lucifer depends so much on which version of the myth or fandom you're pulling from. I'm mostly coming from the 'Supernatural' TV fandom where Lilith is a demon and Lucifer's... well, he's Lucifer, but I've seen a ton of variation. One big plot idea is a kind of cosmic office romance meets rebellion. Think of them as the original power couple who got tired of Heaven's bureaucracy and decided to build their own kingdom—Hell. Fics often explore the early days of that, the arguments over management styles, the slow burn from co-conspirators to partners. It's less about the 'fall' and more about a mutual, deliberate choice to leave. Another popular one is the 'reunion after millennia' trope. Maybe Lilith has been hiding on Earth, living a quiet life, and Lucifer finally tracks her down. The tension there is fantastic—centuries of resentment, maybe a child they had together (often a Nephilim OC), and the question of whether they can rule together again or if they've grown too far apart. I've also seen a lot of fics that flip the script and make Lilith the more powerful, ancient entity, with Lucifer as a later, prideful upstart who needs her wisdom to truly understand his own domain. That power balance shift can be really compelling.
On a more personal, character-driven note, a lot of writers love putting them in surprisingly domestic situations. Like, what does the King and Queen of Hell do on a day off? Do they bicker over the interior design of Pandemonium? Does Lilith get frustrated with Lucifer's dramatic flair when a simple memo would do? I read one fic that was essentially a marriage counseling session between them, mediated by a very brave (or foolish) human therapist. It was hilarious and weirdly touching. The appeal, I think, is taking these larger-than-life mythological figures and grounding their relationship in these petty, human-like disagreements. It makes them feel real. A niche angle I've enjoyed is fics that cross over with other properties, like 'Lucifer' (the TV show) or 'Hazbin Hotel,' where the characters and rules are already so different. In those, their relationship is often framed as a deeply toxic, on-again-off-again mess spanning eternity, which is its own kind of fun to read. You get all the drama without the expectation of a happy ending.