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.
If Merlin died in the fanfiction, it could trigger a series of tragic events. The balance of power could tip, and the villains might seize the opportunity to attack. It could also bring out hidden strengths in the remaining characters as they try to cope with the loss.
In a more humorous take on the 'Merlin tied to a bed' fanfiction, it could be that Merlin has fallen ill and the overly - protective Gaius has tied him to the bed to make sure he rests. Merlin, being the active person he is, complains constantly. Arthur comes to visit and teases Merlin about finally being still for once. Meanwhile, Merlin tries to convince Arthur to let him loose, promising that he'll be fine. Eventually, Gaius relents and unties Merlin, who then immediately starts bustling around the room.
One more idea is that Merlin is tied to the bed in a dream - like state created by an ancient magic. In this dream world, he is faced with his deepest fears and insecurities. His friends in the real world notice his strange behavior and try to wake him up. Merlin, while in the dream, has to find the source of the magic that is binding him and break free. Through his inner strength and the memories of his friends, he manages to do so and wakes up, having learned more about himself and his magic.
If Merlin is a Dark Lord in fanfiction, it could be an interesting exploration of the 'nature vs. nurture' concept. Maybe he turned dark because of the constant fear of being discovered and persecuted for his magic. His actions as a Dark Lord might include taking over Camelot or exacting revenge on those who wronged him in the past. It gives a whole new perspective on his character.
One possible reason could be a magical curse. In many Merlin fanfictions, magic is often used as a plot device. A dark sorcerer might cast a spell on Merlin to make him forget certain things, perhaps to prevent him from using his powerful magic to oppose them. Another reason could be a self - imposed forgetting due to trauma. Merlin has witnessed and endured a great deal of pain and suffering. To protect his own mental state, his mind might subconsciously block out certain memories.
Perhaps some of the snooty nobles who look down on Merlin and constantly try to get him into trouble. They could be making fun of his clumsy ways one too many times and he just snaps and hits them with a shoe. It would be a moment of satisfaction for the readers who don't like those arrogant characters.
He could become a Dark Lord due to betrayal. If someone he trusted deeply, like Arthur perhaps, turned on him because of his magic, it might push him over the edge.