The main characters would be Giovanni for sure. Since he's raising Ash, he'll be constantly interacting with him, guiding him or perhaps manipulating him. Then there are the other Team Rocket grunts. Ash might interact with them in a more friendly or at least respectful way compared to how he does in the normal series. Also, Professor Oak could be in the story. When Ash meets him, it could be a moment of self - discovery as he realizes there's a different world outside of Giovanni's influence.
Definitely his adoptive father, Giovanni. Also, the members of Team Rocket like Jessie and James would probably have a different relationship with Ash. They might see him as a sort of prodigy or future leader. And his original friends like Misty and Brock might cross paths with him, which would lead to some very tense and interesting interactions.
Giovanni is the obvious one. But also, I can see Ash interacting with some of the more powerful trainers in the Pokemon world that Giovanni wants him to either defeat or ally with. For instance, Lance. Ash's interaction with Lance could be very different in this fanfiction. Maybe he's sent by Giovanni to spy on Lance or learn from him. And of course, his friends from his journey. Their interactions would be full of shock and confusion as they see Ash on a different path under Giovanni's care.
Obviously, Ash and Arceus are the main characters. Ash is the one being raised, and Arceus is the one doing the raising. But there could also be other Pokémon that are important in Ash's upbringing, like the Pokémon that Arceus assigns to look after Ash or be his companions during his growth.
Ash is the protagonist who has traveled across different regions, made friends, and trained his Pokémon. Giovanni, on the other hand, is the antagonist, controlling Team Rocket's operations. In the fanfiction, other characters like Ash's Pokémon, Pikachu for example, can also play important roles as they support Ash in his encounters with Giovanni. Also, sometimes characters from Team Rocket like Jessie and James might be involved, either helping Giovanni or getting in the way in some comical or plot - relevant ways.
The main characters would surely be Ash and Mewtwo. But there could also be other Pokemon that play important roles. For example, Pikachu might have a different relationship with Ash since Ash was raised by Mewtwo. And perhaps some of Mewtwo's clones could also be involved, adding more depth to the story.
Well, perhaps in the fanfiction, Ash is raised by Giovanni in a world where the Pokemon League is more corrupt. Ash might be trained to take over the League for Giovanni's benefit. He could then meet his old friends and have to choose between his loyalty to Giovanni and his true friendships. It would make for a very complex and interesting story.
Well, aside from Ash and Giratina, there could be other Pokémon that are part of Giratina's realm. They might interact with Ash during his upbringing and play important roles in his development. Also, Ash's friends from his previous adventures might make an appearance later in the story, either to try and bring Ash back to the normal Pokémon world or to learn from his new experiences.
Some fanfictions might have Misty betray Ash. Perhaps she gets lured by the promise of power or some valuable reward. She could be tricked into believing that Ash is no longer the friend she thought he was and that betraying him is for the greater good.
Jessie and James are the obvious ones. They are the main members of Team Rocket. Jessie could be constantly trying to outdo Ash in Pokémon battles or contests of skill. James, on the other hand, might be more conflicted about having Ash around. He could secretly admire Ash's kindness towards Pokémon and start to have second thoughts about their Team Rocket activities.
Obviously, Naruto and Erza would interact a great deal. Naruto would also probably interact with Erza's friends from Fairy Tail. He might meet Natsu and they could have some interesting battles or friendly competitions. He could also interact with Lucy, and perhaps learn about celestial spirits from her.
Gary Oak is a likely character. He has always been a rival to Ash and in fanfiction, he might betray Ash out of jealousy or a desire to be the ultimate Pokémon trainer. Another could be Misty. Maybe she gets influenced by some external force or her own insecurities and turns against Ash. Brock could also be a candidate in some stories. If he falls in love with a girl who has a vendetta against Ash, he might be forced to choose between his loyalty to Ash and his new love interest.
In 'ash son of lugia fanfiction', Ash is the central figure. But other important characters would include his friends from the original series like Misty and Brock. They could react in different ways to the revelation of Ash's heritage. Also, there might be new characters introduced, such as other descendants of legendary Pokémon. These new characters could be friends or foes to Ash, adding more complexity to the story. And we can't forget about Team Rocket. They might have new motives when it comes to Ash being Lugia's son.