Luke in Percy Jackson fanfiction can play various roles. He could be a reformed villain, seeking to make amends for his past actions. This gives a new arc to his character that wasn't fully explored in the original books.
A common theme could be redemption. Since Luke made some bad choices, a fanfic could focus on his journey towards redemption. Percy could play a key role in this, either by being the one to offer forgiveness or by being the example that makes Luke want to change.
One aspect that could be explored in a Percy Jackson and Luke fanfic is their opposing views. Percy stands for the good, while Luke turns to the dark side. A fanfic could delve into what might have made Luke change his path if Percy had intervened earlier. It could show their early interactions at Camp Half - Blood and how Percy's loyalty and Luke's growing resentment were seeded.
Chiron, the centaur mentor at Camp Half - Blood, might get involved in the rescue. He has a vast knowledge of the demigod world and could use his wisdom and connections to track down Luke and free Percy. Also, some of the other demigods at the camp who look up to Percy might volunteer to help, like Clarisse. She may not like Percy much, but she wouldn't want a fellow demigod to be in the hands of Luke.
There's also 'Fusion of Foes'. This fanfiction is unique because it combines elements of magic and mystery. Percy and Luke find themselves in a situation where they must use their combined powers to solve a mystery that could destroy their world. The relationship between them is portrayed in a very engaging way, with lots of banter and moments of mutual respect that develop throughout the story.
Fanfiction about Percy Jackson and Luke often delves into their dynamic. Luke's betrayal in the main series is a big event. In fanfiction, writers might rewrite this relationship. They could show Luke's earlier days with Percy, how they might have been friends before things went wrong. There could be stories where Percy tries to convince Luke to come back to the right side, exploring themes of forgiveness and redemption. This gives readers a different perspective on the characters and the world of Percy Jackson.
Another great author is 'MythologyFanatic'. They are good at incorporating other mythologies into the Percy Jackson universe in their fanfictions. When it comes to Luke - Percy stories, they often add new elements from different mythologies that make the relationship between the two characters even more interesting and complex.
Percy often gets angry at first. He's not the type to just take it lying down. But he also feels a bit confused as to why Luke is being so mean. Sometimes he tries to stand up to Luke, but other times he just withdraws into himself, feeling sad and alone.
Yes, there are some. You can start by looking on popular fanfiction websites like Archive of Our Own. There you might find various interpretations of their relationship in a gay context. However, the quality can vary greatly, so it's important to read reviews or summaries first.