Well, it depends on your definition of 'good'. Some might focus on the complex relationship between Petunia and the magical world in the context of Harry Potter, while others might take a more creative or off - beat approach. You really have to dig through different works to find one that suits your taste. There could be some that explore Petunia's character in depth, perhaps showing her envy of the wizarding world in a new light, or creating a scenario where she has a more positive interaction with the magical elements, which could be quite interesting to read.
It's inappropriate. The Harry Potter series is mainly aimed at a wide range of audiences, including young readers. Lemon fanfiction strays far from the family - friendly and magical essence of the original. Petunia, as part of the Muggle world related to the story, should uphold a certain standard, and using such fanfiction is not in line with that.
By focusing on their shared past traumas. For example, both have had experiences related to Lily's death in different ways. Harry lost his mother, and Petunia lost her sister. They could start to bond over this common pain and gradually move towards a more positive relationship.
One common theme could be the exploration of Petunia's hidden feelings. Maybe she has some repressed emotions towards the wizarding world that are brought to the surface.
I'm not sure if there are 'popular' ones in the sense that they are widely known and accepted. Lemon fanfictions are a bit of a niche and often not mainstream due to their mature content. But there might be some that have a following within the more hardcore Harry Potter fanfiction community.
Fanfiction can cover a wide range of themes, but 'Harry Potter x Petunia' with a 'lemon' aspect is not something that aligns well with the overall tone of the original story. The series is mainly about magic, friendship, and the fight against evil. If you're interested in their relationship, look for fanfictions that explore their family dynamic, like how Petunia's jealousy and fear influenced her treatment of Harry, rather than 'lemon' ones.
The fact that Petunia uses Harry Potter lemon fanfiction might be a sign of her repressed feelings towards the magical world. In the books, she has a complex relationship with the wizarding side of things. By reading this type of fanfiction, she could be unconsciously trying to come to terms with her own connection to that world. It could also be that she's simply interested in the creativity of the fans, as lemon fanfiction often takes the original story in very unexpected and sometimes racy directions, and she wants to see how far fans are willing to go with their imaginations.
There could be a fanfiction where Petunia Dursley discovers some hidden magic within herself and this somehow links her more closely to Harry. In this scenario, the story could take on a whole new dimension. But as for a particular 'Harry Potter and Petunia Dursley lemon fanfiction', it's hard to point out one without really searching through various fanfiction sites. Also, remember that lemon content often implies sexual undertones which may not be appropriate for everyone.
There could also be other characters from the original Harry Potter series popping up. For instance, Dudley might be in there, and his relationship with both Harry and Aunt Petunia could be explored further in the context of this fanfiction. And of course, depending on the direction of the story, some of Harry's friends from Hogwarts like Ron or Hermione could make an appearance, especially if the story involves the wizarding world interfering with Aunt Petunia's life.
In a more comical plot, the lemon could be a mischievous magical object that keeps causing chaos in Petunia's house. It might make things float or turn into strange creatures. Petunia, being the uptight person she is, has to deal with this lemon - induced mayhem while also trying to keep up appearances in front of the neighbors. This could lead to some really funny situations and a change in her attitude towards the strange and magical over time.