godlike Percy fics often revolve around a few core tensions. His Olympian heritage clashing with the League's mortal-focused idealism is a big one. He might see their no-kill rule as naive, especially if he's coming off a brutal war like in 'The Last Olympian'. That conflict drives a lot of philosophical debates, which can be fun if written well. Another huge theme is legacy and mentorship. You get a lot of fics where Percy, as a god or demigod with centuries of experience, ends up guiding younger heroes like Robin or Superboy, teaching them about sacrifice in a way Batman or Superman might hesitate to. It's about passing on a different kind of wisdom.
Power dynamics are obviously central. How does a being who can control oceans and shake continents fit into a hierarchy with Superman and Wonder Woman? Does he join, or does he operate as an independent, almost mythic force they have to negotiate with? I've read a few where he's treated as a natural disaster they have to contain, which flips the whole superhero narrative. The 'fish out of water' element is there, but it's less about him adjusting to their world and more about them realizing their world has ancient rules they never understood.
Honestly, the best ones ditch the simple power fantasy. They use his divinity to explore alienation—what it means to watch mortals you care about age and die while you remain. A story where the League has to confront the fact that their new ally isn't just powerful, but fundamentally other, can be haunting. The themes aren't always executed perfectly, but the potential is definitely there.