Luke might hold Percy captive to gain some sort of leverage. Maybe he wants to use Percy as a bargaining chip with the gods or Camp Half - Blood. He could be thinking that by having Percy in his hands, he can force the others to give in to his demands.
Well, it depends on the specific fanfiction. Sometimes, Percy might get help from an unexpected source. He could befriend a magical creature that is also held captive by Luke and together they come up with an escape plan. He might also discover a hidden passage or weakness in Luke's lair that he can use to his advantage. Another possibility is that his friends from Camp Half - Blood somehow find out where he is and stage a rescue mission.
One possible motive could be protection. Annabeth might think that there is a threat to Percy that she can only handle by taking him away from the situation. For example, if there's a prophecy that puts Percy in danger and she believes she can keep him safe in a hidden location.
Another motive could be a difference in ideology. If Percy believes in a different way of handling things compared to Artemis, and he feels that her methods are endangering the world or his loved ones, he might decide to betray her in order to stop her from following her current path.
One possible motive could be miscommunication. In fanfiction, if there's a misunderstanding between them, Percy might lash out and seem like he's bullying Annabeth. For example, if he misinterprets her actions as a betrayal, he could start being mean to her.
Maybe he wants to change the system. Percy has always been a bit of a rebel, and in fanfiction, he could see the gods' rule as corrupt or unfair. So, killing them could be his way of starting anew and creating a better world for demigods and mortals alike. Another motive could be to prevent a greater evil. If he discovers that the gods are planning something that would destroy the world, he might decide that killing them is the only way to stop it.
One possible motive could be to create a really dark and edgy take on the characters. Maybe the writer wants to explore how far the characters could be pushed out of their normal personalities. For example, if Percy was under some kind of dark magic influence, it could lead to such an out - of - character action.
One possible motive could be extreme depression. If Percy has been through a lot of hardships in the story, like being ostracized or constantly failing in his goals, it could lead him to this drastic step.
Well, without having read the 'holding you captive novel', it might be a thriller where the main plot revolves around someone being held against their will. It could also be a love story where one person feels 'held captive' by their love for another in an intense way. There are so many possibilities.
One possible plotline could be that Luke has been corrupted by some dark force, and Percy has to fight him to save their world. Percy might be reluctant at first because they were once friends, but the greater good forces him into action.
Luke might become more enraged. Since Percy has thwarted his plan to do something to Annabeth, he could seek revenge. He might start plotting more devious schemes against Percy and Annabeth, or even their friends.