Create a situation where they are forced to rely on each other. Maybe they are trapped in an enchanted place together. During this time, they have to communicate and understand each other better. The daughter could learn about Lucius's past and the reasons behind his actions, and Lucius could see his daughter in a new light.
Have the daughter be a contrast to Lucius in terms of her beliefs. As she tries to sway him towards a more positive path, they engage in intense debates. These debates can gradually transform into a deeper understanding between them. For instance, if she believes in the power of love and friendship, and he scoffs at it at first but then starts to consider it because of her.
At first, Lucius might be shocked by Hermione's flirting. He's used to a certain type of pure - blooded behavior, and Hermione, as a Muggle - born, is completely different. But as she continues to flirt, he could become intrigued. He might start to see her in a new light, not just as a Mudblood but as an intelligent and alluring witch.
Their relationship could start with hostility. Lucius might initially try to undermine Hermione's efforts in some wizarding matter, but she outsmarts him every time. This could gradually turn into a begrudging respect as he realizes her intelligence. For example, in a magical research competition.
Well, it might start off very coldly. Lucius would be reluctant to accept help from a mudblood like Hermione in his eyes. But Hermione, being persistent, would keep pushing to help him. As she starts to break down his walls, Lucius might find himself drawn to her in a strange way. Maybe he starts to see her as a powerful ally rather than an inferior. And Hermione might start to understand the pressures that made Lucius the way he was before. This could lead to a relationship that has elements of mutual understanding, respect, and perhaps even a bit of attraction as they both discover new sides of each other during their time together.
Their relationship might develop through a series of intellectual debates. Hermione is known for her sharp mind, and Lucius is no fool either. They could start arguing about topics like blood purity and the rights of different magical beings. These debates could lead to a grudging respect for each other's viewpoints, and from there, a more positive relationship could start to form.
At first, their relationship might be filled with distrust. Hermione would be suspicious of Lucius' motives since he has a history of being a Death Eater. Lucius, on the other hand, might see Hermione as just a task he has to fulfill. But as they interact more, for example, when Lucius helps Hermione with her studies of some complex dark magic related knowledge (but in a non - evil way), they start to understand each other better.
Their relationship could start out as a sort of alliance based on their families' pure - blood legacies. But as they get to know each other better, they might find that they have more in common than just blood status. Draco could be intrigued by the mystery of voldemort's daughter, and she might be drawn to Draco's complex personality.
The relationship might start with Lucius seeing an opportunity in Harry's new identity. He could try to manipulate Harry at first. But Harry, being Harry, might resist and gradually turn the tables. They could end up in a power struggle within their relationship.
In canon, Harry and Lucius are enemies. But in a Fem Harry Potter scenario, the relationship could start off with Lucius underestimating her because she's a girl. This could lead to her getting the upper hand in some initial encounters. For example, she might use her charm or a different kind of magic that Lucius isn't expecting. Their relationship could develop into a more complex dance of power and manipulation compared to the straightforward enmity in the original story.
By having them share common goals. For example, if there's a powerful artifact that both want to keep out of the wrong hands. This would force them to interact and start to understand each other's motives.
Their relationship could start with mutual suspicion. Harry is wary of Evangeline because she's a Malfoy, and Evangeline is hesitant about Harry due to his reputation as the 'Chosen One'. But as they are forced to work together on a school assignment, they start to see each other's true natures. They gradually become friends and confidants, sharing their fears and hopes.