The real story of Lucy Gray is often associated with the poem by William Wordsworth. In the poem, Lucy Gray is a young girl. She wanders out into a snow - storm one day. Her parents search for her but she is never found alive. It's a rather melancholy tale of a child lost in nature.
One common theme is survival. Lucy Gray's story in the original context is about survival in a harsh environment, and fanfictions often expand on this. For example, she has to use her wits and skills like singing to stay alive.
They might love fanfiction because it offers new and different perspectives on their own world or relationships. Fanfictions can take the existing characters and settings they are familiar with and twist them in interesting ways.
It could be another dark guild. They might be using Gray as a pawn to kidnap Lucy, perhaps because they know of her celestial spirit magic and want to use it for their own evil purposes. Gray may not be fully aware of their manipulation.
One possible plot could be that Gray kidnaps Lucy as part of a misguided attempt to protect her from an unknown danger. He might think that by taking her to a secluded place, he can keep her safe from a powerful enemy that is targeting her.