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.
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.
One possible fanfic could be about Petunia Dursley finding a magical toy that once belonged to Harry Potter's parents. Maybe she discovers it in the attic and it starts to show her memories of Lily and James Potter. She realizes that she has been wrong about Harry all along and decides to change her attitude towards him.
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.
A possible plot could be a time - travel scenario where Harry and Petunia are sent back in time. They have to rely on each other to survive in the past, and in the process, they learn more about their family history and each other. This shared adventure could lead to a deeper understanding and a different kind of relationship between them.
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.
Finding 'Harry Potter x Petunia Dursley' lemon fanfiction might be a bit tricky. First of all, the relationship between them in the original series is quite antagonistic. And secondly, 'lemon' content often goes against the terms of many platforms. But if you really want to look for it, you could join some Harry Potter fanfiction communities and ask around, though you may be met with some disapproval due to the nature of the content. Fanfiction should ideally be about exploring different aspects of the characters in a more positive and non - inappropriate way.
A fanfic could connect them by having a toy that was passed down from Lily Potter to Harry, but Petunia has kept it hidden all these years. When Harry discovers it, it causes a big conflict as Petunia doesn't want to let go of the last piece of her sister she has in that way. But eventually, it could lead to a moment of reconciliation between them.
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.
One good aspect is the exploration of their family ties. Petunia is Harry's aunt, and despite her coldness, there could be a deeper connection beneath the surface. Another aspect is how Petunia's Muggle perspective clashes with Harry's magical world.