One potential kidnapper could be a dark wizard who wants to use Lucy's Celestial Spirit keys for their own dark magic. Another could be a rival guild member who is jealous of Lucy's power and wants to steal her keys to gain an advantage in the magical world. It could also be someone from Lucy's past, like an old acquaintance who has turned bad and has some grudge against her.
One possible plot development could be that the guild members quickly realize Lucy is missing and start a search. Natsu, being her closest friend, might lead the charge. They could follow any clues left behind, like a piece of Lucy's clothing or a strange magical residue. Another development could be that the kidnappers demand a ransom from the guild in the form of a powerful magical item. The guild then has to decide whether to give in or find another way to rescue Lucy. Or perhaps Lucy manages to escape on her own using her Celestial Spirit powers. She could call upon one of her spirits, like Leo, to help her break free from her bonds and then find her way back to the guild while avoiding the kidnappers.
Yes, there are likely fanfictions with such a plot. Fanfiction often explores different scenarios and relationships within the 'Fairy Tail' universe. However, not all of them are well - written or in line with the original spirit of the series.
In a fanfiction where Lucy is kidnapped, the Fairy Tail guild would likely spring into action. Natsu, being her closest friend, would be furious and determined to find her. He'd probably charge off without much of a plan, with Happy flying after him trying to keep him in check. Gray would also be involved, using his ice - magic to combat any obstacles in their way. Erza would lead the strategic part of the rescue mission, planning their every move carefully.
In some fanfictions, if Natsu kidnapped Lucy, it could be a comical situation. Natsu might do it out of his own strange sense of protecting Lucy in an overzealous way. Maybe he thinks there's a danger that only he can keep her safe from, and his impulsive nature leads him to this 'kidnapping' which is more like a forced protection.
One way it could end is with a big showdown. The Fairy Tail guild members find the kidnappers' lair, and there's an epic battle. Natsu defeats the main kidnapper with his powerful fire magic, and Lucy is freed. Then they all return to the guild, where there's a big celebration.
She might use her celestial spirits in unexpected ways against the guild. For example, she could have her spirits create illusions to embarrass the members.
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.
Another scenario could be a misunderstanding within the guild. Maybe a new member misinterprets Lucy's actions as a threat and attacks her. In the heat of the moment, before the situation is clarified, Lucy gets beat up. This could lead to a story arc about resolving misunderstandings and building trust within the guild.