In fanfiction, it might be due to a redemption arc for Lucius. He realizes the error of his ways in the wizarding war and starts to view Hermione, a muggle - born with great talent, as someone worthy of protection. He could also be protecting her from other dark wizards who might want to harm her because of her intelligence and influence among the light - sided wizards. This protection could also be a form of self - atonement for his past misdeeds against the muggle - borns.
The theme of unexpected alliances is also common. Lucius and Hermione are not characters one would expect to be on the same side. But in these fanfictions, his protectiveness creates an alliance between them. This alliance might be formed due to a common enemy, or a shared goal that they discover along the way. It makes for an exciting read as they navigate their relationship while dealing with the outside forces.
There's a lesser - known one called 'Lucius's New Focus' which has Lucius being protective of Hermione in a world where the wizarding politics are more convoluted. The story shows how Lucius, who is often seen as a villain, starts to see Hermione in a different light and decides to keep her safe from the chaos that ensues in the magical world.
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.
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.
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.
In fanfiction, the relationship between Hermione and Lucius can be quite complex. Some fanfictions might explore a scenario where they are enemies forced to work together due to certain circumstances in the wizarding world. For example, they could be paired in a mission to save Hogwarts from a new dark threat. Their different backgrounds, Hermione being a Muggle - born Gryffindor and Lucius a pure - blood Slytherin, would create a lot of tension and interesting character dynamics.
Another idea is that Hermione is there by accident. She could have been exploring the Malfoy Manor (where Lucius's office is located) out of curiosity or in search of something related to Harry Potter's past. Once in the office, she discovers a hidden secret about the Malfoy family that could change the course of the wizarding war.