Perhaps Bellatrix was forced into a situation by Voldemort. He might have wanted to create a new heir or a special pawn in his game. He could have used some form of mind control or coercion on Bellatrix to make her have a child. And this child, Harry, could have been part of a grand plan that Voldemort had. Or it could be that Bellatrix had a change of heart at some point, met someone she loved, and against all odds, had Harry, but still had to deal with her past as a Death Eater.
Maybe it was a last - minute decision by James and Lily. They might have thought that having Bellatrix as a godmother would offer some kind of protection. After all, she was a powerful witch. Or perhaps there was some sort of old family pact or agreement that made her the godmother.
One possible plotline could be that Bellatrix captures Harry during one of his adventures and decides to keep him as a pet for her own amusement. She might use dark magic to bind him and make him obey her commands. Another could be that in an alternate reality, Harry is somehow magically enslaved to Bellatrix from the start, and the story follows his attempts to break free from her control while she uses him for various dark purposes, like spying on the Order of the Phoenix.
A possible plotline could start with Bellatrix having a strange fascination with Harry from the start. She manages to get him in her clutches and treats him like a pet. Harry, on the other hand, uses his wits and the limited magic he can access in this state to outsmart Bellatrix. There could be a lot of psychological battles between them, with Harry trying to understand Bellatrix's twisted mind while she tries to break his spirit. And all this could be set against the backdrop of the ongoing war between the good and the evil in the wizarding world.
One scenario could be that a powerful magic spell backfires and turns Bellatrix into a small animal that Harry then takes in as a pet. Another could be that in an alternate universe created in the fanfiction, the power dynamics are so different that Bellatrix is somehow subjugated to Harry and made into his pet.
Harry might become more conflicted. Knowing Bellatrix is his aunt could make him question his own identity and his place in the wizarding world. Bellatrix, on the other hand, could start to have doubts about her loyalty to Voldemort. This new family connection might tug at her conscience, if she has any left.
One possible plotline could be that Harry discovers the truth slowly. At first, he might notice strange similarities between himself and Bellatrix or some unexplained magical abilities that seem to link him to her. This discovery could throw him into an identity crisis as he has always thought of himself as an orphan with no real family other than the Dursleys.
Hermione could be an ally. Hermione is known for her intelligence and open - mindedness. She might see the potential in Bellatrix's daughter to change and be a force for good. She could help the daughter learn about the positive aspects of magic and the wizarding world.
Well, there could be themes like the power of love to overcome differences. Harry is a symbol of good and Bellatrix of evil, so a fanfiction might explore how love can bridge this huge gap. Also, themes of self - discovery for Harry, as loving someone like Bellatrix would make him question his own values and beliefs. This kind of fanfiction would likely have complex character development to make such an unusual relationship seem plausible.
Another possibility is that Bellatrix is being controlled by an even more powerful and mysterious force. This force wants Harry Potter to be saved for its own purposes. Bellatrix is just a tool in this situation. The fanfiction could explore how she struggles against this control while still fulfilling the task of saving Harry.
One possibility is that it could be a result of some powerful magic gone wrong. Maybe she was involved in a spell that was supposed to do something else but ended up changing her hair color to white. It could also be a sign of her having a special connection to an ancient magic that is associated with white - haired beings in the wizarding world.