Well, perhaps Laxus has some misguided notion that Lucy has information vital to the guild's safety. So he kidnaps her thinking he can extract it from her quickly. But in reality, Lucy has no such information and she has to convince Laxus of that.
Laxus could be seen as the main antagonist in this scenario since he is the one who kidnaps Lucy. However, it could turn out that there is a greater force behind his actions, in which case that unknown entity would be the true antagonist.
Well, it could be that Lucy has a misunderstanding. Maybe she overhears something that makes her think Natsu is planning to leave the guild without saying goodbye. So, in a fit of panic and anger, she kidnaps him to get an explanation. Then, as the story progresses, they have a heart - to - heart conversation where the misunderstanding is cleared up. It could also be a situation where Lucy is competing with someone else for Natsu's attention, and she thinks that by kidnapping him, she can have him all to herself for a while and figure out how to make him like her more.
It could be another guild that sees Natsu as a threat. They might find out about Lucy kidnapping Natsu and try to use the situation to their advantage. For example, they could try to steal Natsu's magic or get information out of him while he's in a vulnerable state. Another possible antagonist could be a character who has a grudge against Lucy. They might try to stop her from getting away with the kidnapping or use it as a way to get revenge on her.
The story might end with Sarah actually falling in love with Jareth. She decides to stay in his world and they rule the Goblin Kingdom together, bringing a new era of peace and harmony between the human world and the Goblin realm. This would be a very different ending from the more common 'escape and return home' trope.
It could also end with a more complex resolution. Loki realizes the error of his ways during the time he has Tony kidnapped. Maybe through their conversations, Loki sees the value in Tony's life and the good he does. So, Loki releases Tony and decides to help the Avengers in their fight against a common enemy as a form of redemption.
It could end with Lily escaping and being forever angry with Snape. She might cut all ties with him and go on to marry James Potter, with Snape left full of regret for his actions.
There's not enough information to really know who Lucy specifically is. She could be just a regular reader of fanfiction who took the time to rate this piece as M. Maybe she's part of a fanfiction community where people rate works to help others know what to expect.
One idea could be that the Joker kidnaps Batman to force him into a series of cruel 'games'. Maybe he wants Batman to choose between saving his closest allies or innocent civilians, testing his moral limits.