One common theme is identity. Since Percy has two very different divine parents, he often struggles to figure out who he really is in fanfictions. Another theme is power. With the combined powers of Lupa and Poseidon, his power levels and how he uses them are often explored. Also, acceptance by his peers is a big theme as they may view his dual heritage as strange or overpowering.
Maybe Percy discovers a prophecy that involves both his father Poseidon and Lupa. He has to journey to different realms under the sea and in the Roman wolf - related places. Along the way, he meets new demigods and creatures that either help or hinder him in fulfilling the prophecy.
I've heard of a fanfiction called 'Percy's New Path'. In this story, being the son of Lupa and Poseidon gives Percy some extraordinary powers that he has to learn to control. It also delves into his relationships with his friends and how they react to this new revelation about his parentage. It's quite an engaging read.
In this fanfiction, there might be a lot of focus on Percy's relationship with the other wolves in Lupa's pack. He could learn their ways of survival, their hierarchy, and how to be a part of their community. This would be a great way to explore his adaptability and growth.
Lupa herself would be a major character. She's the one who has a special connection to Percy in this story. She could be guiding him, testing him, or having her own motives that are intertwined with Percy's journey.
The setting of the story might shift a bit. Instead of always being at Camp Half - Blood or on quests related to the Greek gods, Percy could be in the territory of the wolves. There could be new threats and challenges there, like rival wolf packs or ancient enemies of Lupa. And all these elements would make for an exciting and different take on the Percy Jackson universe.
A prevalent theme is isolation. In many fanfictions, Percy feels alone because of his strange heritage. He doesn't quite fit in with the normal demigods. Also, the theme of destiny often comes up. He has a special destiny due to his parents that he is constantly striving to fulfill.
I've read a fanfiction where Percy is the son of Lupa and Chaos and it focuses on his relationships. 'Percy's Bonds' is the name. It shows how his different heritage affects his friendships and romances, and how he has to come to terms with who he really is in the context of his relationships.
One interesting plot could be Percy having to prove himself to Lupa's pack in a series of dangerous trials. Maybe he has to hunt a mythical beast that has been terrorizing the pack's territory.
There's also a fanfic called 'Poseidon's Promise'. In this one, Percy has to deal with a mysterious prophecy related to his father. The story is full of twists and turns. It delves deeper into the relationship between Percy and Poseidon, which is really interesting to read about. It also has some great action scenes with Percy using his water - based powers.