It could be a way to show a completely different side of Petunia. In the original, she's quite harsh towards Harry. As a pet, she might be more endearing and protective, which would be a huge contrast.
Well, it depends on the specific fanfiction. Some fanfic authors like to play around with the relationships and concepts in the Harry Potter universe. So it's possible that in certain fanfictions, Petunia is Harry's pet. However, in the canon story, Petunia has a very different role as Harry's rather unfriendly aunt who begrudgingly takes him in. But fanfiction allows for all kinds of creative interpretations.
In some fanfictions, Voldemort's pet might be used as a symbol of his power and evil. Harry's glasses, on the other hand, are an iconic part of his character. The combination could be used to create a unique plot. For example, Voldemort's pet might steal Harry's glasses to disrupt his vision and thus his ability to fight. It could also be a more symbolic connection, like the pet representing Voldemort's hold over Harry's life, and the glasses being a symbol of Harry's identity that Voldemort wants to break.
Well, in such a fanfiction, Petunia might finally come to terms with Harry's wizarding world. Maybe she starts to see the magic in a new light and reconciles with the fact that her sister was a witch.
Petunia Dursley is significant as she represents the non - magical world's reaction to magic in the Harry Potter series. She is a Muggle who has a complex relationship with the magical world. She has seen magic through her sister but resents it. Her actions towards Harry, like treating him as an outcast in her home, show how some Muggles might fear or be envious of the magical abilities they don't possess.
Perhaps the plot could involve Petunia having some sort of magical awakening or discovery that leads her to perform this transformation on Harry. In this fanfiction, Harry might then use her new female identity to infiltrate parts of the wizarding world that are more difficult for a male to access, like certain all - female magical groups. And this could lead to all sorts of adventures and revelations about the wizarding world's gender dynamics.
One possible plot could be that Harry shows a special talent early on that Vernon and Petunia recognize as something extraordinary. This makes them see Harry not as a burden but as a valuable part of the family. They then start to love and protect him, and this changes Harry's life completely. He no longer has to endure the abuse and neglect he faced in the original story.
I'm not entirely sure as 'lemon' often implies adult content in fanfiction, but if we assume it's a non - adult take, perhaps Harry could dominate Petunia in terms of magical knowledge. Maybe he shows her the true power of magic and she has to accept his superiority in that regard.
One possibility is that Petunia could use her witch powers to protect Harry secretly. Maybe she has a change of heart after years of resentment. She could have been in contact with the wizarding world all along, but hid it from everyone. This would add a whole new layer of mystery and family drama to the Harry Potter universe.
The plot could start with Petunia having a strange encounter with an angel. The angel seems to know things about her past and her relationship with Lily. At the same time, an elf, which has been observing Petunia for some reason, decides to approach her. The angel wants to help Petunia understand the importance of magic and her family's place in it. The elf provides some practical help, like getting access to some magical items. As the story progresses, Petunia changes her view of the wizarding world, and together with the angel and the elf, they might even influence some of the events in the wizarding world, like helping to protect Hogwarts or something similar.
One possible plot could be that Petunia is somehow magically enslaved by a dark wizard. Harry, upon finding out, feels a sense of obligation to save her. He might have to use his knowledge of magic and his connections at Hogwarts to figure out a way to break the spell. Along the way, he could discover some secrets about Petunia's past that were related to the wizarding world.