Perhaps in this fanfiction, Naruto's connection to Lucifer is a secret kept by a few powerful beings. As he grows stronger, he starts to show signs of Lucifer - like abilities such as the ability to manipulate shadows in a more sinister way. This causes his friends to be both curious and a bit afraid of him. Naruto then has to figure out how to control these new powers and keep his relationships intact.
His character would likely face an internal struggle. On one hand, he has his values of friendship and protecting the village. On the other, he has this new relation to Lucifer which could bring out a more power - hungry side. For instance, he might be tempted to use Lucifer's powers for personal gain rather than for the good of all. He would have to constantly battle this internal conflict and decide who he really wants to be.
Often, they feature Issei with enhanced powers due to his Lucifer connection. This can lead to more epic battles and power - up moments. The stories may also delve deeper into the lore of the devil world, exploring things that the original series only hinted at.
Yes, there are quite a few. You can find some on fanfiction.net. Just search for 'Highschool DxD Issei Lucifer' and you'll get a list of stories. Some of them might focus on Issei's growth as a devil with his Lucifer powers, while others could be about his relationships in a more in - depth way.
Issei Hyodo is often a popular choice. His unique ability as a 'Boosted Gear' wielder and his growth throughout the original series make him an interesting character to include in fanfiction. He can bring a lot of action and his relationships with other characters can be explored further.
One idea could be a new character joining the school who has a mysterious power that both the devils and angels are interested in. This new character could disrupt the existing power balance in the school.
A common theme is the clash of different moralities. Naruto is from a world with a strong sense of right and wrong, while Lucifer has a more complex moral standing. Another theme could be power exchange. Maybe Naruto is offered power by Lucifer in exchange for something.
One plotline might be that the Naruto universe and Lucifer's world collide. Naruto teams up with some of Lucifer's allies (or enemies) to save both worlds from a common threat. For example, a powerful demon from Lucifer's world is trying to invade the ninja world, and Naruto, with his new - found knowledge of Lucifer's powers and the underworld, has to lead the charge to stop it.
Well, one possible plot could be that Harry discovers his true heritage as Lucifer's brother. This could lead to a conflict within him as he tries to reconcile his life as a wizard with this new, dark family connection. Maybe he has to face some sort of magical or otherworldly council that is worried about the implications of having Lucifer's brother in the wizarding world.
Well, in this fanfic scenario, Naruto's ninja skills could be a huge asset in the High School DxD world. He might introduce new combat styles and strategies. For example, his shadow clone jutsu could be used in various battles or for pranks. Also, his strong sense of justice would likely influence Rias and her peerage. He could help them make more morally upright decisions, and his experience with facing powerful enemies in the Naruto universe would give them new perspectives on handling threats in their own world.