It could be about Acnologia teaching Lucy some powerful magic. Maybe he sees potential in her and decides to train her in combat magic. For example, he might show her how to better control her celestial spirits in battle situations.
It's possible that in this fanfiction, Lucy and Acnologia meet in a neutral territory. Lucy, with her kind heart, tries to communicate with Acnologia. Acnologia, who has been alone for a long time, is initially hostile. But as Lucy persists, she manages to break through his tough exterior. They might then share stories about their pasts, with Lucy talking about her guild and Acnologia about his past as a dragon.
Maybe there's a group of dragon hunters. They view Acnologia as the ultimate prize and would do anything to capture him. When they see Lucy interacting with Acnologia, they consider her a traitor to humanity and try to take them both down. They could be the main antagonists as they constantly pose a threat to Lucy and Acnologia's new - found relationship.
One common theme could be growth. Laxus might be training Lucy to help her grow stronger in terms of her magical abilities. Another theme could be friendship. Through the training process, they could develop a deeper bond as friends.
Lucy could become more confident. With Acnologia's training, she might gain a new level of self - assurance in her abilities. For instance, she could stand up to stronger opponents without hesitation.
The 'lucy trains with the dragons fanfic' might revolve around Lucy's journey of self - discovery through training with dragons. Dragons are often symbols of power and mystery in fantasy. So, perhaps Lucy starts off as an ordinary person, but as she trains with the dragons, she discovers hidden powers within herself. She could be training to become a dragon rider, which would require her to learn how to communicate with the dragons, understand their behavior, and master the art of flying on their backs. It could also include elements of her facing challenges within the dragon community, like dealing with rivalries among different dragon groups.
It could also be that Acnologia has some sort of vendetta against a particular member of the Fairy Tail guild who is close to Lucy. By kidnapping her, he aims to draw that person out and seek revenge. He might believe that this is the best way to get to his real target.
Well, you can try searching on popular fanfiction websites like FanFiction.net or Archive of Our Own. Just type in 'laxus trains lucy' in their search bars, and you'll likely find a bunch of stories. However, the quality can vary greatly, so be prepared to sift through some to find the really good ones.
The guild as a whole would likely mobilize. Erza would start formulating a strategic plan. She'd consider the strengths and weaknesses of Acnologia and figure out the best way to approach the situation. Gray would also be ready to fight, using his ice - make magic to support the rescue mission. They would all be united in their determination to get Lucy back safely.