There might be some out there, but it's a rather unusual pairing considering Vernon's often cruel treatment of Harry in the original series. Fanfiction can take all sorts of creative turns, though. You could try searching on popular fanfiction websites like Archive of Our Own or Fanfiction.net. However, this pairing goes against the typical relationship dynamic presented in the Potter books.
One main theme could be redemption. Since Vernon was so mean to Harry, a fanfiction might explore how he redeems himself through love. Another theme could be the power of love to change relationships. It could show how their relationship evolves from hostility to love.
One interesting fanfiction could be about Vernon Dursley having to face a magical threat in the Muggle world on his own. He might have to rely on some of the little knowledge he has about the wizarding world through Harry. Another could be a story where Vernon and Harry are forced to work together during a crisis that affects both the Muggle and wizarding communities, changing their relationship completely. There could also be a fanfiction exploring Vernon's past and how it might have influenced his treatment of Harry, and then how things could have been different if certain events in his past were changed.
One interesting fanfiction could be about Vernon Dursley's perspective during the time when Harry first received his Hogwarts letter. It might explore his extreme reactions and the inner turmoil he felt at the thought of magic being real. Another could focus on a situation where Vernon has to interact with the wizarding world in an unexpected way, like when he accidentally stumbles into Diagon Alley.
One great fem Harry Potter and Vernon Dursley fanfiction is 'A Different Perspective'. It explores how a female Harry Potter might interact with Vernon in a more complex way than in the original series. The author really delves into the characters' personalities and how they would clash or, surprisingly, sometimes find common ground. It's an interesting read that gives a fresh take on the relationship between these two characters.
Redemption is also a popular theme. Writers often like to give Vernon a chance to make up for his years of mistreating Harry. They might show him gradually changing his views and actions towards Harry as he realizes the error of his ways. Another theme is the clash between the Muggle and magical cultures through Vernon's eyes. His strict adherence to Muggle normalcy makes for an interesting contrast when faced with the chaos of the magical world.
I'm not sure of specific 'lemon' fanfictions as they often contain inappropriate content. But there are some great non - 'lemon' fics that focus on their relationship. For example, there are ones that explore Vernon's jealousy towards Harry's magical abilities in a more family - drama - like way.
One great Vernon Dursley fanfic is 'The Unseen Side of Vernon'. It delves into his character in a unique way, showing his insecurities and how his upbringing might have shaped his rather unpleasant personality towards Harry. Another one could be 'Vernon's Redemption Arc' which is an interesting take on him trying to make amends for his past behavior towards Harry.
I'm not really into slash fanfiction myself, but you could try searching on some popular fanfiction websites like FanFiction.net or Archive of Our Own. There might be some unique takes on the relationship between Harry Potter and Vernon Dursley in those platforms.
In many 'Harry Potter x Vernon Dursley fanfic', the theme of growth is prevalent. Both characters can grow and learn from each other. For example, Harry might teach Vernon about the importance of acceptance, while Vernon could show Harry some aspects of the Muggle world he hadn't considered. Also, the theme of power struggle can be seen. Vernon has a certain kind of power over Harry in the Dursley household, and fanfics might explore how that power shifts as Harry grows older and more powerful in the wizarding world. And of course, there's the theme of forgiveness. Given how horribly Vernon has treated Harry in the books, some fanfics will focus on whether Harry can forgive him or not.
Another theme is family. Since they are related, albeit reluctantly in the original story, fanfictions often explore what it means to be family. They might show how Harry and Vernon could form a strange but real family bond.