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.
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.
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 common theme is identity. Percy has to figure out who he is as the son of Lupa, different from his previous identity. Another theme is loyalty, whether it's to his new wolf pack or his old friends.
Another theme is transformation. In many fanfics, Percy's relationship with Lupa causes him to transform, not just in terms of his powers but also his understanding of loyalty and leadership. Lupa represents a different kind of power and wisdom, and Percy has to adapt to that. For example, in some stories, he becomes more in tune with his animal instincts because of her influence. This transformation theme adds depth to their relationship.
Power and identity are common themes. Percy as the son of Chaos has new powers, and he has to figure out how to use them while still being himself. Another theme is relationships. The harem aspect means there are multiple complex relationships to explore.
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.
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.
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.
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.
One common theme is the power of love against all odds. In these fanfics, Percy and Chaos often face many challenges, but their love overcomes them.