Petunia could be a great addition. Her relationship with both Harry and Vernon adds a lot of complexity. She could be the mediator or the one causing more trouble between them, depending on the plot.
Perhaps in the fanfiction, Vernon discovers a hidden magical talent of his own. Harry, upon finding out, has to decide whether to help Vernon develop it or keep it a secret from the wizarding world as Vernon is a Muggle. This could lead to a lot of comical and tense situations.
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 interesting story could be where Vernon Dursley has a sudden change of heart towards Harry Potter due to some magical influence in the fanfiction. Maybe he starts to see Harry's value and tries to protect him from other dark forces in the wizarding world. This would be a great twist on their usually antagonistic relationship.
In some fanfictions, Harry might cope by finding solace in his friends at Hogwarts. He could talk to Hermione and Ron about what Vernon does, and their support gives him strength. For example, they might encourage him to focus on his magic studies as an escape from the Dursley's household.
One common theme is the discovery of love. Since it's about Lily and Vernon, a lot of fanfictions focus on how they come to realize their feelings for each other. It could be a slow - burn process or a sudden realization.
Maybe Vernon is jealous of Harry's magical abilities. He might see Harry as a threat to his 'normal' family image. Also, Vernon has always been a bully at heart and Harry, being an easy target in his house, becomes the victim of his pent - up anger.
One common theme is redemption. Often, Vernon is depicted as having a chance to redeem himself for his past bad treatment of Harry. Another theme is the discovery of common ground. For example, they might find out they both have a love for a certain type of food or a shared fear. And family is also a theme. Despite their differences, they are still family in a way, and fanfictions sometimes explore how that family bond can be mended or redefined.
Perhaps Dudley finally stands up to his father's cruel treatment of Harry. Maybe he realizes that Vernon's behavior towards Harry is wrong and uses his own physical strength or some clever ruse to get Harry out of a difficult situation Vernon has put him in.