One popular fanfiction might be 'A Different Sort of Family'. In this, Lucius starts to see Hermione's intelligence and strength and gradually treats her as a daughter. He begins to protect her from the darker elements in the wizarding world that he is unfortunately a part of. Another could be 'Unexpected Bonds'. Here, Lucius realizes that Hermione has a lot to offer in terms of knowledge and loyalty, and their relationship evolves into a father - daughter like bond over time.
In fanfiction, when Lucius treats Hermione like a daughter, Lucius's character undergoes a significant transformation. He moves away from his traditional pure - blood supremacist views. This new relationship forces him to re - evaluate his beliefs. Hermione, on the other hand, gets to experience a different side of the wizarding world. With Lucius as a sort of father figure, she might have access to knowledge and resources she wouldn't have otherwise. This could make her more well - rounded and less judgmental towards those she previously thought were all bad, like Lucius himself.
Hermione might struggle with her identity. She has been a strong advocate for the rights of Muggle - borns, and now finding out she's related to a pure - blood supremacist like Lucius could cause an internal conflict.
Another plot could involve the daughter discovering a long - hidden secret about her parents' relationship. Maybe there was a prophecy that led to their union, and she has to figure out how to deal with the implications of this discovery. She could be hunted by dark forces who want to use her for their own gain because of her unique heritage.
If Hermione was Lucius' daughter, her relationship with other Slytherins would be complex. Some Slytherins would likely welcome her as a pure - blood heir of the Malfoy family. However, she might also face some jealousy. Her intelligence could be seen as a threat to some of the more power - hungry Slytherins. And given that Hermione has a strong moral compass, she might not fit in completely with the more devious Slytherin crowd. She could be an outcast among them while still being part of the house.
Her character might develop in a way that she constantly tries to prove herself. Because of her parents' polar - opposite reputations, she would feel the need to show that she is not defined by their actions or reputations. She could excel in both academics and magic - related sports, like Quidditch, to gain respect.
Well, in the original 'Harry Potter' series, Lucius Malfoy is a pure - blood supremacist. Hermione is a Muggle - born witch. So in fanfiction, this prejudice might be carried over. He may see Hermione as an inferior due to her non - pure - blood status and thus dislike her.
For Lucius, his development could be a slow process. At first, he resents being around Hermione, but as he witnesses her magic and her kind heart, he starts to question his own values. He may begin to see the error of his ways regarding blood purity. Hermione might develop more patience. Dealing with Lucius, who has such different views, makes her learn to tolerate and try to change someone rather than just oppose them.
Hermione could also use her magic skills to her advantage. She is a powerful witch, and in the Malfoy household, she may use her magic to create a space for herself where she can be true to herself. She might also use magic to subtly influence Lucius and make him more accepting of her and her beliefs.
One interesting plotline could be the clash of their different ideologies. Hermione, with her strong beliefs in equality and justice, and Lucius, from a traditional pure - blood family with elitist views. Their marriage, forced by the law, might lead to a power struggle within the Malfoy household as Hermione tries to assert her values.