Well, there could be a lot of things. Maybe Lucy would show off her new swimsuit and Gray would make ice sculptures on the beach. The Fairy Tail guild members could also have a big barbecue on the beach, with Erza trying to keep everyone in line while they enjoy the food and the ocean view. They might even discover some mysterious sea creature that leads to an unexpected adventure.
You could have a 'Magic Swap' party. In this party, the Fairy Tail members temporarily swap their magic abilities with each other. This would lead to some really funny and interesting situations. Natsu trying to use Gray's ice magic and constantly slipping on his own ice creations, or Erza using Lucy's celestial magic and trying to summon spirits in a very Erza - like strict way.
One interesting plot could be that the Fairy Tail members hold a pool party to celebrate a big victory. During the party, there are various fun competitions like the best pool trick competition. Gray might accidentally freeze part of the pool, causing chaos but also lots of laughter.
Natsu would probably be the most entertaining. His fiery and impulsive nature would lead to all sorts of comical situations at the beach. He might try to swim in lava - like hot water or accidentally burn someone's beach towel while trying to dry himself off.
Happy, Natsu's sidekick, is almost always present in these fanfictions. His ability to fly can add an extra element of fun to the pool party, like dropping water balloons from above. And of course, the guild master Makarov might be involved, either as the organizer or as an observer, adding his wisdom and humor to the whole pool party scenario.
They could interact more casually. In the original series, there are often battles and serious missions. But at a party, they might just joke around and share funny stories. For example, Gajeel and Natsu could have a friendly competition about who can eat the most food at the party instead of fighting over something serious.
It adds more content. The official Fairy Tail series has a limited number of episodes and chapters. Fanfiction fills in the gaps. For example, it can create stories about what the characters were doing during the time - jumps in the original story.
If Lucy never joined Fairy Tail, the friendships and relationships among the characters would form in a very different way. Also, many of the story arcs might not unfold as they do in the original plot.
One popular theme is alternate universes (AUs). Writers like to explore what would happen if the Fairy Tail characters were in different settings, like a modern - day high school or a steampunk world. Another common theme is romance. Fans often pair up their favorite characters in different relationships, such as Natsu and Lucy or Gray and Juvia.
Erza and Jellal are also a favored couple in Fairy Tail fanfiction. Their complex past, with Jellal's redemption arc, adds a layer of depth to their potential relationship. It allows for stories that deal with forgiveness, love that overcomes past wrongs, and the growth of their connection over time. There's also Gajeel and Levy, as their interactions in the series suggest a budding relationship that can be elaborated on in fanfics.