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 are fanfictions where Petunia has a change of heart towards Harry. For example, she realizes the error of her ways after seeing how much danger Harry is constantly in at Hogwarts. She then tries to make amends by secretly helping him, like sending him care packages with useful Muggle items that can be adapted for magical use.
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.
One possible fanfiction could be about Petunia Dursley having a secret love for lemon - flavored treats and how it changes her mood. For example, she discovers a new lemon cake recipe and it makes her momentarily forget her usual grumpiness.
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 interesting 'Harry Potter Petunia Dursley' fanfic could be one that explores Petunia's childhood and how her relationship with Lily might have affected her view of Harry. For example, a fanfic could show that deep down, Petunia was always a bit envious of Lily's magical abilities, but also loved her sister in a complicated way. This envy could have then translated into her cold treatment of Harry.
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.
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.
There might be a fanfiction where the Dursleys are forced to enter the wizarding world due to some magical accident. This could lead to all sorts of comical and tense situations as they struggle to adapt to a world they have always despised. For example, Vernon Dursley having to deal with talking portraits or flying broomsticks.
One popular 'Harry Potter Dursley' fanfiction might be 'The Dursleys' New Perspective'. It delves into how the Dursleys' lives are changed in unexpected ways. Another could be 'Dursley Encounters', which explores their interactions with the wizarding world in a unique manner. There's also 'The Secret of the Dursleys' that reveals hidden aspects of their family.
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.