Harry's Patronus charm, which is a manifestation of positive energy, could have an interesting reaction when in the presence of Lucifer. Since Lucifer is associated with the underworld and negative forces in a way, the Patronus might act as a counterbalance or even a repellent to some of the darker aspects of Lucifer's world. At the same time, Lucifer's power to see people's desires could help Harry understand the motives of his enemies better. For example, if they were facing a dark wizard who had some hidden desires that were fueling his actions, Lucifer could reveal those, and Harry could then use that knowledge to find a way to defeat the wizard using his magic.
One interesting crossover could be a scenario where Harry Potter is transported to Lucifer's world in Los Angeles. Maybe he needs Lucifer's help to defeat a new kind of dark magic that has some connection to the infernal realm. For example, a dark wizard has made a pact with a minor demon and is causing chaos in both the wizarding world and the human world. Harry, with his knowledge of magic, and Lucifer, with his understanding of the supernatural in his own realm, could team up to solve the problem.
They can be combined by having a common enemy. Suppose there is a new dark force that threatens both the wizarding world and Lucifer's world. Harry Potter and Lucifer Morningstar would then have to team up to fight it. This would bring together their different powers and ways of thinking. Also, a character from one world could be cursed to live in the other world, which would create interesting storylines as they try to adapt and find a way back.
Well, in some fanfictions, Lucifer Morningstar could be curious about the magic in the Harry Potter universe. He might visit Hogwarts in disguise and cause chaos. He could interact with Dumbledore, who would be very cautious of him. There could also be a fanfiction where Harry Potter and his friends have to go to Hell (Lucifer's domain) to retrieve a lost magical artifact and face all kinds of devilish challenges along the way.
No. Percy Jackson is a series in its own right with its own unique mythology and characters, having no relation to being a fanfiction of Lucifer Morningstar.
One interesting plot twist could be that Harry's true nature is revealed during a crucial battle. Instead of using his normal wizarding spells, he taps into his Lucifer - given powers and turns the tide in a way that no one expected. But this also makes everyone around him question who he really is.
Well, one way could be by exploring the clash of two very different magical worlds. Harry would have to deal with the expectations of the wizarding world from his Potter side and the dark, otherworldly nature of being Lucifer's son. Maybe he'd have new and strange powers that would both terrify and amaze his friends at Hogwarts.
You can start by looking on popular fanfiction websites like Archive of Our Own (AO3). There are often a plethora of fanfictions involving unique crossovers like Lucifer Morningstar and Loki. Another option is Fanfiction.net, though AO3 generally has a more diverse and inclusive range of works in terms of themes and pairings.
I'm not entirely sure if there is a large amount of it, but given the creativity of fanfiction authors, it's highly likely that someone has written a story where Naruto has some sort of connection to Lucifer Morningstar. It could be a really strange or really cool concept, depending on how the author approaches it. You could also check out some Naruto or Lucifer Morningstar fan forums to ask if anyone knows of such fanfiction.
There's also 'Lucifer's Redemption Arc' which is really interesting. This fanfiction focuses on Lucifer's attempts to fully redeem himself in a world that still has its doubts about him. It has some really well - written dialogue that brings out the essence of the character.