One interesting Darcy and Lizzy fanfiction could be a story where they meet in a modern setting. For example, at a university. Darcy might be a reserved yet brilliant student, and Lizzy could be the outspoken and intelligent girl in the literature class. They start off on the wrong foot, just like in the original, but their relationship develops as they work on a group project together.
A great one is where Lizzy is a detective and Darcy is a suspect in a case. At first, Lizzy is convinced of his guilt, but as she digs deeper, she realizes there's more to him. This flips the dynamic between them and adds an element of mystery to their relationship.
Lizzy might be a person who has had a significant impact on the author's life. She could be a neighbor who was always there to help, and over time, the narrator developed deeper feelings for her. It's also possible that she's someone the author met during a trip, and they had a special connection from the start.
She might survive by making use of her relationships. For instance, if she has some sort of connection with Loki (maybe from past encounters), she could call out to him telepathically (if there's some sort of magic involved). Loki, being the trickster he is, could then come and rescue her. Another way is that Darcy could use her knowledge of science to create a makeshift weapon or a device that would help her escape from Hydra's clutches. She could use the materials available in her cell to build something useful.
Ciel would likely become more protective. He has always been in a dangerous world, and now with a baby on the way, he'll do whatever it takes to safeguard his family. Lizzy, she might become more nurturing. She was already a strong character, but motherhood could bring out a softer, more patient side of her.
Another reason could be that fanfiction gives them a sense of community. By loving and reading fanfiction, they can connect with other fans who have similar interests. They can discuss their favorite stories, share their thoughts on different interpretations of their characters, and feel part of a bigger group.
One of my favorite scenes in Ciel x Lizzy fanfiction is when Lizzy stands up for Ciel in front of others. It shows her loyalty and her growth from a somewhat sheltered girl to someone who can be a protector. Another great scene is when Ciel lets his guard down a little around Lizzy, like sharing a quiet moment in the garden. It's a rare moment of vulnerability for him.
In Kuroshitsuji fanfiction, Ciel and Lizzy often have a complex relationship. Lizzy is initially presented as a somewhat naive girl, but she has a deep affection for Ciel. Their relationship can be seen as a blend of childhood friendship and something more. Ciel, on the other hand, is burdened with his revenge and his role as the Earl. Sometimes, in fanfiction, their relationship is explored in different ways, such as Lizzy becoming more aware of Ciel's true self and trying to support him despite his dark secrets.
Darcy could also be a bit annoyed at times. She's a smart and capable woman. So when the Avengers are overly protective, like not allowing her to go to a certain place for her research because it's 'too dangerous', she might try to argue her case. However, deep down she knows they mean well and it's their way of showing they care.
She also adds a different perspective as a scientist. The Avengers are often focused on the combat and heroics side of things. Darcy can remind them of the scientific implications of their actions. Like when they are dealing with a new form of energy, she can explain how it could affect the environment or civilians in the long run.