Well, obviously she'll interact with her past self. It would be really interesting to see how she reacts to seeing a younger and more naive version of herself. She could also meet characters who are no longer alive in the present. For example, if there were any great wizards from the past who played important roles in the history of magic. Additionally, she might cross paths with some of the villains from the past who were causing trouble long before the current villains in the story. This could change her perspective on the whole conflict in the present.
There's also 'Lucy's New Beginnings'. This one is about male Lucy starting his journey in the magical world in a completely different way than in the original story. He meets different characters first and forms unique alliances. It's a long - form fanfiction that really develops his character well.
One great 'Lucy Heartfilia hurt' fanfiction is 'Bleeding Heart'. In this story, Lucy gets injured during a battle with a powerful dark wizard. The author does a wonderful job of portraying her pain and the concern of her guild mates. It really delves into her character and shows her strength even when she's physically and emotionally hurt.
Death the Kid would be an extremely interesting character for Lucy to interact with. His obsession with symmetry and his powerful abilities as a meister could lead to some really unique scenarios. Lucy might be both fascinated and a bit put off by his quirks at first. But as they get to know each other, they could learn a great deal from one another. For example, Death the Kid could help Lucy understand the importance of precision in combat, which could enhance her use of celestial spirit magic, while Lucy could introduce him to the concept of celestial spirits and their different powers.
Another theme is the support of her friends. In many of these fanfictions, when Lucy is hurt, her Fairy Tail comrades come to her aid. It emphasizes the strong bonds within the guild and how they care for each other.
One interesting plot twist could be that when Lucy goes back in time, she discovers that her family has a much darker secret than she ever knew. Maybe they were involved in some sort of magic that was considered forbidden in the past. Another could be that she accidentally changes the future in a way she didn't expect, like making her friends not become the people she knew them as. And perhaps she finds out that an enemy in the present was actually once an ally in the past, and she has to figure out what went wrong to turn them into an enemy.
It gives writers the chance to explore different relationships. For example, how male Lucy would interact with the male characters in a different way than the female Lucy did. Maybe he has a different kind of bromance with Natsu or a more competitive relationship with Gray. It just adds a whole new layer to the story.
One reason is that the original story of Lucy Heartfilia has a lot of potential for expansion. Fans love to see different scenarios for her. In fanfiction, they can put her in unique situations, like time - traveling or meeting alternate versions of her friends. Moreover, her character development in the official story is something that fans want to continue in their own ways through fanfiction, which is why it's so popular.
Yes, there are quite a few out there. You can start by looking on popular fanfic websites like Archive of Our Own. Just search for 'luffy x lucy heartfilia' and you'll find a variety of stories with different plotlines and writing styles.
Another fanfic could focus on Lucy's relationship with Erza. Maybe they team up for a tournament within the Fairy Tail guild. Along the way, they face tough opponents and have to rely on each other's strengths. Lucy's strategic thinking combined with Erza's powerful combat skills would make for an exciting story.