One implication is that it would completely change Hermione's backstory. Instead of being a Muggle - born witch, she would now have a pure - blood family connection. This could lead to a different perception of her among the wizarding community.
In fanfiction, anything can be possible. Writers often create such unexpected relationships for the sake of creativity. Maybe the author wanted to explore a different dynamic between Hermione and the Malfoy family. It could lead to some really interesting plot twists, like how Hermione would interact with Draco knowing she's Lucius' sister, and how that would change the whole Hogwarts power dynamic.
Well, if Hermione was Lucius Malfoy's sister in fanfiction, it would completely turn the story upside down. First, Hermione's loyalty to the Gryffindor values would be in a huge conflict with her Malfoy family ties. She might be pressured to side with the Death Eaters or at least be more sympathetic to their cause which she would resist. Second, her relationship with Harry and Ron would be strained. They might not trust her as easily, thinking she could be a spy for the Malfoys. And third, it would change her entire backstory. Instead of being a Muggle - born witch, there would have to be some sort of complex family history to explain her connection to the pure - blood Malfoy family.
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.
Fanfiction about Hermione and Lucius can be quite interesting. Writers might play with the concept of redemption for Lucius. Maybe Hermione sees a side of him that others don't. It could also be a way to explore power dynamics in a new context, with Hermione's intelligence and Lucius's former status in the wizarding world.