He could be a bit surprised at first, but then a warm feeling would spread through him. He might gently stroke her hair or cover her with a jacket if she seemed cold, all while having a soft smile on his face.
Maybe she had a long day of training or adventuring. She could have been mentally and physically exhausted from dealing with various challenges in their world, like fighting monsters or solving complex puzzles.
One possibility is that they've had a long and tiring adventure. After facing numerous challenges, they find a moment of peace and Annabeth, exhausted, falls asleep on Percy. It could also be a sign of their deep trust in each other. In fanfiction, this might be used to show the closeness of their relationship.
Annabeth is known for her intelligence and strategic thinking. She is a strong and independent character. Percy, on the other hand, is brave and has a strong connection to the water due to his father being Poseidon. In the fanfic, when Annabeth sits in Percy's lap, it might be a way to show their unique relationship which has developed over the course of their many shared experiences in the Percy Jackson universe.
Some characters might find it cute. For instance, Grover could just smile to himself seeing how close his friends are. He might even be a bit envious of their relationship.
Percy might feel a deep sense of contentment. He and Annabeth have a special bond, and having her trust him enough to sleep in his lap could make him feel warm and happy inside. He may also feel a bit nervous, not wanting to move and disturb her peaceful slumber.
One possible scenario could be that they are on a long journey and Annabeth is exhausted. Percy offers his lap as a place for her to rest, showing his care for her. Another might be after a difficult battle where Annabeth is drained, and Percy's lap becomes a safe and comfortable place for her to recover.
Well, it could be a sweet moment of relaxation. Maybe they've just had a long adventure and Annabeth is exhausted. Percy is just there, being a comforting presence as she takes a nap on his lap. It shows their closeness and trust in each other.
Perhaps they are in a romantic setting. They could be sitting by a campfire at Camp Half - Blood, and Annabeth spontaneously sits in Percy's lap as a sign of their growing affection for each other. This could lead to a sweet moment of them sharing stories or just enjoying each other's company in a more intimate way.