Their relationship might start off rocky. Percy has had his fair share of problems with Hera in the original stories. But in the fanfic, as they face challenges together related to the lemon element (maybe it's a cursed lemon grove they have to save), they could gradually learn to respect each other. Hera might see Percy's courage and loyalty, and Percy might see a different side of Hera that is more vulnerable.
In this fanfic, their relationship development could be quite complex. Hera, being a powerful goddess, and Percy, a demigod hero. The lemon aspect could be a catalyst. For example, if the lemon has some sort of magic that only Percy can control and Hera needs it for a particular reason. At first, Hera might try to manipulate Percy to get it. But as Percy resists and they engage in a battle of wills, they start to understand each other on a deeper level. This could lead to a transformation in their relationship, where they become partners in a truer sense, with mutual respect and a new - found understanding.
It could develop in a really interesting way. Since Hera is the goddess of marriage and Percy has his own ideas about relationships. Maybe the lemon in the fanfic represents something that binds them, like a shared goal that is symbolized by the lemon. As they work towards that goal, their relationship could shift from hostility to a sort of begrudging alliance, and then perhaps into a real friendship where they trust each other and rely on each other's strengths.