Lucius may become more conflicted. He starts off as a loyal Death Eater, but having Harry in his care makes him question his loyalty to Voldemort. He might start to see the humanity in Harry and that could soften his cold - hearted nature. For example, he may find himself protecting Harry from other Death Eaters.
In such fanfictions, Lucius might show his protection by shielding Draco from the Dark Lord's direct orders. For example, he could try to find ways to delay or modify tasks assigned to Draco that are too dangerous. He may also use his influence within the Death Eater ranks to keep Draco out of harm's way.
He might be shocked at first. Since Lucius is a complex character, he could initially see it as a weakness in Harry that he could potentially use to his advantage in the wizarding world's power games.
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.
They could start by having an honest conversation. Lucius needs to admit his wrongdoings and Draco needs to express his pain. It's a first step towards redemption.
Harry would probably be extremely cautious. He has a strong sense of right and wrong, and Lucius has been on the wrong side in his eyes. Harry would be analyzing Lucius' every move, trying to understand if this is some sort of new Dark Arts plot or if there's something else going on. He would also be worried about the implications for his friends and the wizarding world in general.
Harry might start as a reluctant follower of Voldemort in the fanfiction. As time goes on, he could either become more hardened by the dark environment or find a way to subvert it from within. Lucius, who was already a Death Eater, may develop a more complex relationship with Harry. He could initially see Harry as a threat to his status with Voldemort but later come to respect Harry's strength and cunning.
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.
Lucius has a sense of entitlement that comes from his pure - blood upbringing and family wealth. Hermione, being a Muggle - born (in the original story), has had to fight for her place in the wizarding world. So in fanfiction as siblings, Lucius might initially look down on Hermione's more inclusive views, while Hermione would be appalled by Lucius's prejudice. However, as the story progresses, they could learn from each other. Lucius could become more open - minded and Hermione could understand the pressures of a pure - blood family.
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.