He could betray Naruto to Orochimaru. Orochimaru is always looking for powerful allies and new test subjects. Lucifuge might be lured by Orochimaru's promises of power and knowledge. Orochimaru could use Lucifuge to get closer to Naruto in order to steal the Nine - Tails' chakra or some other valuable asset.
Finding good Grayfia Lucifuge fanfics, especially those with a 'lemon' aspect (which often implies a more adult - themed or romantic/sexual content in the fanfic world), can be a bit tricky. Some dedicated fanfic communities might have such works. For example, Archive of Our Own (AO3) has a large collection of fanfics, but you need to be cautious as there are rules and guidelines regarding appropriate content. Also, the perception of what makes a 'good' fanfic in this context can differ from person to person, depending on their interests in the characters, the writing style, and the plot development.
Well, Naruto is obviously one of the main characters. He's the protagonist of the Naruto series, and in the fanfiction involving Lucifuge, he's likely to be at the center of the story, dealing with the new elements related to Lucifuge. And then there's Lucifuge itself, which is the new and mysterious element introduced into the Naruto universe in this fanfiction. It could be a character with its own motives and powers.
The world in which Grayfia exists is full of magic and intrigue. Fanfiction writers can build on this world, adding their own details and plotlines. They can create stories that focus on her role in the grand scheme of things, or they can zoom in on her personal growth and development. All these elements combined make 'grayfia lucifuge fanfiction' very appealing.
One interesting Naruto Lucifuge fanfiction could be about Naruto somehow getting in touch with Lucifuge's powers and how he uses them in the Naruto universe. Maybe he uses these new powers to face stronger enemies in a unique way.
In a Naruto Lucifuge betrayed fanfiction, the betrayal could be part of a much larger conspiracy. Lucifuge might be under the control of a powerful dark force. He betrays Naruto not out of his own will, but because he is being manipulated. This could lead to a journey for Naruto to not only stop Lucifuge but also to find a way to free him from the control of this dark force. Naruto would have to face his own feelings of trust and friendship being broken while also trying to save his friend from the clutches of evil.
One popular 'grayfia lucifuge fanfiction' might be 'Grayfia's Secret Mission'. It delves into her character in an interesting way, showing her loyalty and hidden strengths. Another could be 'Grayfia in the Human World' which explores how she adapts to a completely different environment.
Before reading such fanfics, know that 'lemon' usually indicates mature content. So, make sure you are of an appropriate age and comfortable with that kind of material.
Another way is to focus on their relationships. Have them interact with different characters from Highschool DxD. If they form a friendship with Issei, they could learn about human values from him, which would contrast with their demon upbringing. Or if they have a rivalry with another demon, it could push them to become stronger. Also, let their relationships change over time, like starting as enemies and then becoming allies.
One idea could be that the Lucifuge OC has a hidden power that gets awakened during a major battle at the school. Maybe it's a power related to time manipulation which could turn the tide of the fight against a powerful enemy.