It might also just be a normal part of their relationship. If the fanfic is set in a world where they are very comfortable with each other, it could just be a casual display of their closeness without any major relationship shift, but still showing how important they are to each other.
It can be a sign of their growing intimacy. In a relationship, such actions are often markers of a deeper level of closeness. It might also make their relationship more public within the Hogwarts community, as others would see this display of affection.
They could become even closer friends. After going through the war together, they have a deep bond. Maybe they start to rely on each other more than ever, sharing every little detail of their lives.
If Harry Potter is sitting on a professor's lap in fanfiction, it could transform their relationship in several ways. Firstly, it might make their relationship more like a family bond, especially if the professor has been acting as a mentor. Secondly, it could create some jealousy among other students or even some of the professors. Thirdly, it could make Harry more confident in seeking the professor's help in future situations, knowing that there is this special connection. Overall, it would add a new layer of complexity and closeness to their relationship.
It's hard to say exactly what would happen. Maybe it would create tension, or it could be a moment of closeness and realization. The possibilities are endless based on how the author wants to take the story.
Some writers do it to create a sense of shock or surprise. It's a bit out of the ordinary for their relationship as shown in the official series. By having Hermione sit on Harry's lap, it grabs the reader's attention and makes them wonder what's going to happen next in the story. It could be a starting point for a whole new plotline or a development in their relationship.
One possibility could be a moment of comfort. Maybe they are in a dangerous situation and Hermione is scared, so she sits on Harry's lap for a sense of security. Harry then consoles her and they share a deep, platonic moment.
As Hermione comforts Harry, they start to develop a more intimate bond. Harry begins to understand Hermione's caring nature on a deeper level. He realizes that she is always there for him, no matter what. This makes him more protective of her as well. For example, in a dangerous situation, he might be more concerned about her safety because of the special connection they've developed during these comforting moments.
Their relationship might become more intimate. This simple act of Annabeth sleeping on Percy's lap can break down some barriers between them. It shows a level of vulnerability from Annabeth and a protective side from Percy.
At first, it would be really rocky. Harry has a history of distrusting Snape, and Hermione might be a bit cautious too. But as time passes, Snape's care for them in his own strict way would start to show. He'd probably be tough on them about their studies, but they'd see it's because he wants them to succeed.
It could symbolize a strong bond between them. Dumbledore is like a father figure to Harry, and this physical closeness shows the level of trust and affection Harry has for Dumbledore and vice versa.