In some fanfictions, Acnologia is made out to be Natsu's father. But this is not part of the original canon of the Fairy Tail series. Fanfiction writers often like to create such unexpected family relationships to add new twists to the story.
In many Fairy Tail fanfictions, the battle between Natsu and Acnologia is often depicted as extremely epic. Natsu's fiery determination and his unique dragon - slayer magic make for an interesting contrast against Acnologia's overwhelming power. Some fanfictions might have Natsu discover new forms or powers in order to stand a chance against the fearsome Acnologia.
A common theme in such fanfictions is Natsu's unwavering courage when facing Acnologia. He might not be as strong as Acnologia at first, but his will to protect his friends and the Fairy Tail guild drives him forward. His dragon - slayer magic could potentially have some hidden aspects that are only revealed during this encounter.
One possible plot could be that female Acnologia, being a powerful and feared being, initially sees Natsu as an enemy due to his association with the dragon slayers. But as they cross paths more often, she starts to notice his determination and the kindness in him. Eventually, they team up against a common greater evil, and during their adventures, a romantic bond slowly forms between them.
Since 'lemon' fanfiction has adult - oriented elements, I can't really point you to any. Instead, consider looking for stories that focus on the character development of Natsu and Acnologia. For example, stories about their battles together, or how they might overcome their differences in a non - sexual way. You can start by using search terms like 'Natsu and Acnologia character study' on different fanfiction websites.
His confidence might become more of an overbearing arrogance. Since Acnologia is so powerful, Natsu could start to think he's invincible after being trained by him. He might become more solitary too, as Acnologia is often depicted as a lone figure. Natsu might start to distance himself from his Fairy Tail friends because he feels he's on a different level now.
If Natsu were trained by Acnologia, he might face a moral dilemma. Acnologia is a feared and often seen as an evil force. Natsu has always been on the side of good. So, during the training, he would have to decide whether to follow some of Acnologia's more ruthless ways of using power or stay true to his own values. This internal struggle could add a lot of depth to his character. Also, his relationships with his friends in Fairy Tail might be strained as they might be worried about the influence Acnologia has on him.
Maybe Natsu and Acnologia could meet in a different dimension where they both lose their memories. They have to figure out who they are and how to get back home. Along the way, they form an unlikely friendship as they discover their hidden powers in this strange new world. This could be a story full of mystery and self - discovery for both characters.
It could be Zeref. Since Zeref has an interest in powerful magic users and Natsu is a strong dragon slayer, Zeref might kidnap Natsu to study his magic or use him in some dark plan related to his quest for immortality or power.
Natsu was walking through the forest one day when suddenly a group of dark mages emerged from the shadows. They quickly overpowered him with some sort of magic -binding spell. They dragged him away to an old, creepy lair. His friends back at the guild soon realized he was missing and set out on a search mission. Happy flew around frantically looking for any sign of his friend. Lucy, Gray and Erza teamed up and followed some leads they found in the forest. They were determined to rescue Natsu no matter what it took.