It could be that in this particular fanfiction, the writer has a different vision for Lucy's character development. Perhaps they think she can grow more independently outside of Fairy Tail. There might also be some plot twists that prevent her from joining, like she has a prior obligation to another group or person that conflicts with joining Fairy Tail.
One reason could be that the author wants to create an alternate universe where Natsu has a different path. Maybe in this fanfiction, he has a prior commitment to another guild or group that prevents him from joining Fairy Tail.
Well, in fanfiction, Lucy might be crying because she lost a fight against a powerful enemy. Maybe she felt she let her friends down. For example, if she was unable to protect someone important in the story, it could lead to her breaking down in tears.
The story could also revolve around how the guild members' relationships change. For instance, Happy might not be as cheerful without Natsu around. And the guild as a whole might become more united in trying to find a replacement for Natsu or trying to figure out how to move forward without him. They could start to explore different parts of the magical world to find new allies or magic that can help them in their battles.
In this fanfiction, the story might take a darker turn. Natsu is like the heart and soul of Fairy Tail in many ways. Without him, there could be a sense of gloom in the guild. However, this could also be a catalyst for change. Characters like Wendy could step up more. She might start to explore and master her dragon slayer magic in ways she hadn't before. And the relationships between the characters would shift, perhaps becoming more complex as they deal with the absence of Natsu.
Perhaps in the fanfiction's plot, Natsu makes a big mistake that endangers Lucy or her friends. Let's say he recklessly takes on a powerful enemy without a proper plan, and Lucy's friends get hurt as a result. This might cause her to hate Natsu for his irresponsible behavior.
A possible reason could be personal conflicts within the guild. Lucy might have an issue with some of the guild's rules or how certain things are run. Juvia could be following Lucy for some reason, like loyalty or because she also has her own issues with the guild. For instance, if there are tensions between Juvia and other members over Gray.
He could kidnap her because he believes she's in immediate danger. Natsu is very impulsive and might not have time to explain things properly, so he just takes her away to keep her safe.
Maybe they leave because they want to search for answers about their pasts. Happy might want to know more about his origins, and Lucy could be seeking something related to her family's history.
In fanfiction, Lucy might want Natsu because of their strong bond. They've been through many adventures together. Natsu is always there to protect her, and his brave and fun - loving nature attracts Lucy.
One popular 'End Join Fairy Tail' fanfiction might be 'The New Adventure'. It often features new characters joining the Fairy Tail guild and going on unique quests. Another could be 'End Join: The Power Within' which focuses on the development of the joined characters' powers within the Fairy Tail universe.