Yes, there might be such fanfictions out there. The Harry Potter fandom is quite large and diverse, and fans often come up with unique and unexpected relationships in their fan - created stories. You can try searching on popular fanfiction websites like Fanfiction.net or Archive of Our Own.
It's hard to say for certain. The Harry Potter fanfiction community is vast and diverse. Some writers like to create alternative universes where characters have completely different relationships. But given the nature of Harry and Lucius in the original series - one being the hero and the other a Death Eater - making them brothers would require a great deal of imagination and explanation. The writer would need to explore how this new relationship would affect the plot, the other characters, and the overall themes of the story. It might also change the way we view the magical world's social and political structures as they are presented in the books.
One possible plot could be that Harry grows up in the Malfoy family. He might be treated differently from Draco, as he has different values. This could lead to internal family conflicts. Harry could try to use his influence within the family to change their dark views. Maybe he secretly helps the Order of the Phoenix while still being part of the Malfoy family.
Sorry, I don't know of any specific fanfiction with that plot. You could try searching on popular fanfiction websites like Archive of Our Own or Fanfiction.net. Use keywords like 'Harry Potter Lucius brother' in the search bar to see if you can find what you're looking for.
I'm not sure specifically if there are a large number of such fanfictions, but given the vast and diverse nature of the fanfiction community, it's very possible. It could be an interesting concept to explore, as it would completely change the power dynamics, the nature of Harry's relationships with Draco and other characters, and how the wizarding world views him. It might also lead to some really unique plotlines involving the Malfoy family's politics and their role in the wizarding world.
Hermione could be a great addition. She could be the voice of reason when Harry starts getting closer to Lucius. Her intelligence and knowledge of magic could also help in any situation they face together. Another good character would be Draco. Since Lucius is his father, it would add an interesting dynamic. Draco could be conflicted about his father's new relationship with Harry. And of course, Dumbledore. His wisdom and guidance could play a crucial role in how the relationship between Harry and Lucius develops.
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.
One great 'Harry and Lucius Fanfiction' is 'The Unlikely Alliance'. It shows an interesting dynamic where they are forced to work together against a common enemy. The author does a great job of exploring their complex relationship.
Lucius' need in Harry Potter fanfiction could be power. He was always power - hungry in the original books. In fanfiction, this could be explored further. For example, he might try to find new dark magic artifacts or form new alliances to gain more power. He could also need revenge. If he feels that certain characters, like Harry Potter or the Weasley family, have humiliated him or his family, he would seek revenge in various creative ways that fanfiction writers can come up with. Maybe he would use his wealth and influence to undermine their reputations or set up elaborate traps for them.