He might be initially startled. Arthur is used to a certain propriety in the court, so having Merlin suddenly on his lap would catch him off - guard. But then, depending on their relationship at that point, he could either laugh it off if they are in a very friendly stage or he might be a bit flustered and ask Merlin to get up if there are other people around.
One possible plot could be a moment of deep friendship. Maybe they are in a private chamber, discussing a serious matter about the kingdom. Merlin, in his eagerness or perhaps to show his loyalty closely, sits on Arthur's lap. They then have an intense conversation where Merlin reveals some hidden knowledge or a plan to save Camelot from an upcoming threat.
Merlin would be very worried. He would probably stay by Arthur's side day and night, using his magic secretly to try and heal him. He might also search for rare herbs or magical items that could cure Arthur.
Arthur might be initially shocked and confused. He's used to Merlin being in control. But then he might find it quite hilarious and start teasing Merlin about it.
He might also get angry. Merlin has his own pride and after all he has done for Arthur, being insulted like this would make him furious. He could start yelling back at Arthur, listing all the times he has saved Arthur's life or the kingdom.
Merlin might be initially shocked and heartbroken. He has been so close to Arthur, and this sudden forgetfulness would be a huge blow to him.
The physical closeness of Merlin sitting on Arthur's lap can be the start of a deeper emotional connection. Arthur might become more aware of Merlin's vulnerability, which could lead to him being more open and caring towards Merlin in general. For example, he could start sharing his own insecurities with Merlin.
Merlin could be heartbroken. He might retreat into himself and become more withdrawn. After all, he has a deep bond with Arthur, and this sudden break - up would be a huge shock.
In some versions of this type of fanfiction, Arthur's reaction is complex. He might be stunned into silence when he first finds out. His mind would be racing with thoughts about all the times Merlin has used his magic to save him or Camelot without his knowledge. After the shock subsides, he may have a heart - to - heart with Merlin. They would talk about the implications of the secret, and Arthur would likely start to view Merlin in a whole new light, as not just his servant but as a powerful ally with a great burden.
A possible plotline could be a moment of comfort. For example, if Hermione is upset or stressed, she sits on a friend's lap (maybe Harry or Ron) for solace and they have a heart - to - heart conversation. Another could be a romantic plotline where she sits on the lap of a love interest as a flirtatious or affectionate gesture, leading to a deeper exploration of their relationship.
Merlin would likely be seen as a bit of an enigma at Hogwarts. His magic is different from the norm, so he might be a bit of an outsider at first. But his kind heart and loyalty would soon win over his classmates. Arthur would be the brave and headstrong character, perhaps a bit like a Gryffindor version of his usual self. He'd be eager to learn about combat magic and would probably be a natural leader in group projects or Quidditch teams.