I'm not sure specifically as there could be many different interpretations in different fanfictions. But generally, it might involve Luke taking actions to rescue Percy from some sort of danger, like a monster attack or a dangerous situation in the world of their story.
Well, in this 'luke saves percy fanfiction', it could be that Luke has had a change of heart. Maybe he realizes that Percy is important for some greater good in their fictional realm. He might save Percy from a powerful enemy that Percy couldn't handle on his own. For example, if Percy was trapped by a group of particularly strong mythological creatures, Luke could use his skills and knowledge to get Percy out of there. It could also be a more complex situation where Luke is trying to make amends for past wrongs by saving Percy.
You could try searching on popular fanfiction websites like Archive of Our Own (AO3) or FanFiction.net. Just type in 'luke saves percy' in the search bar, and it should show you relevant stories if they exist.
Another place to check is FanFiction.net. There are many Percy - related fanfictions there. Just be sure to use the search function to narrow down to the 'Percy Saves Luke' ones. Sometimes you might need to browse through different categories related to the Percy series to find the specific fanfic you want.
One interesting 'Percy Saves Luke' fanfiction could be where Percy uses his unique powers over water to rescue Luke from a sinking ship. In this fanfic, Percy might have to battle some sea monsters along the way.
Redemption is a huge theme. Vader, who has been on the dark side, choosing to save Luke represents his chance at redemption. Another theme is family. Despite all the conflict, the bond between father and son is strong enough for Vader to turn around and save Luke.
I don't know for sure as I haven't read this particular fanfiction, but usually in fanfiction, Percy could be a character from a popular book, movie or TV series.
The theme of power is also common. Both Percy and Luke are powerful in their own ways. Fanfictions may explore how they use or misuse their power, how they compare to each other in terms of strength, and how they learn from each other's approach to power.
Redemption is also a big theme. Luke made some bad choices, and fanfiction often explores if he can be redeemed, with Percy sometimes being the key to that redemption. It gives a chance to rewrite his story in a more positive light.
If Luke were good, it could completely change the dynamics of the story. Maybe he'd become a powerful ally instead of an antagonist.
At first, it could be quite rocky if they find out later in the story. Percy might be angry that Luke has been keeping secrets or has done bad things in the past. But eventually, they would likely grow closer as they realize they are family and start to support each other.
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.