It depends on the specific fanfiction. While the base material of Dragon Slayer might not have Levy as a Dragon Slayer, in the world of fanfiction, all kinds of alternate storylines are possible. Some writers may see her character as having the potential to take on this role and create a whole new set of adventures and relationships around it.
One possibility could be that they start their journey by accidentally stumbling upon a hidden dragon lair. Inside, they find ancient scrolls that teach them the basics of dragon slaying. Lucy might use her celestial magic in unique ways, like summoning spirits with dragon - like abilities to aid her in combat. Levy, with her script magic, could decipher the secrets of dragon weaknesses written in long - forgotten languages on the scrolls.
One unique aspect could be her use of her book - based magic in a new way. As a Dragon Slayer, she might incorporate her knowledge of ancient texts into her dragon - slaying techniques. For example, she could use spells from old books to enhance her attacks or defenses against dragons.
Maybe they are caught in a magical experiment gone wrong. The experiment was aimed at creating artificial dragon slayers, and Lucy and Levy end up being the accidental subjects. Their existing magic gets combined with dragon - slaying magic. Lucy's celestial spirits might be enhanced with dragon - slayer - like traits, and Levy's script magic could start to incorporate dragon runes that give her the power to harm dragons. They then have to figure out how to control these new and unexpected powers while on their journey to become full - fledged dragon slayers.
Levy's character could be developed by showing her growth from a sheltered princess to a strong and independent woman. For example, through her interactions with Gajeel, she might learn to be more assertive. Gajeel, on the other hand, could start as a rough - around - the - edges dragon but become more gentle and caring as he gets closer to Levy.
You can try fanfiction websites like Archive of Our Own (AO3). It has a large collection of fanfics, and you might be able to find some great 'levy dragon slayer fanfic' there.
One great 'levy dragon slayer fanfic' could be about Levy going on a quest with the dragon slayers to find a lost magical artifact. The story might focus on her using her intelligence to solve various puzzles along the way.
One great Levy the Dragon Slayer fanfiction could be 'Levy's Hidden Adventure'. It might explore her unearthing some ancient magic that no one knew about. Another could be 'Levy and the Lost Dragons', where she forms an unexpected bond with a lost dragon species. There could also be 'Levy's New Magic', which focuses on her developing a unique form of magic.
Their relationship can be developed through shared experiences. For example, they could be on a mission together where they have to rely on each other's strengths. Gajeel's physical power and Levy's intellectual power would complement each other, and this would lead to a deeper understanding and respect between them.
One interesting plot idea could be that Gajeel discovers a new type of dragon magic that only Levy can help him understand. Maybe it's a magic that involves ancient dragon runes, and Levy's knowledge of books and languages is crucial in deciphering it. As they explore this new magic together, their relationship deepens.