Well, it creates drama. Readers like to see their favorite characters in difficult situations. When Percy is wrongly blamed, it makes us feel for him and root for his vindication.
It could be Chandler. He's always been a bit of a bully in the Loud House universe. With Lincoln having powers, Chandler might become jealous and try to find a way to take those powers away or use them for his own bad purposes.
One possibility is that Lincoln could get super strength. He might use this power to protect his family from various threats in Royal Woods. For example, he could stop a runaway car that was about to hit his sisters.
His siblings could be responsible. They are always getting into crazy situations together, and maybe one of their pranks or games goes too far and accidentally hurts Lincoln.
One great 'Percy gets wrongly blamed' fanfiction is 'The False Accusation'. In it, Percy is wrongly blamed for stealing a powerful artifact. The story then unfolds as he tries to clear his name while also dealing with the real culprit who is trying to frame him further.
Well, in this fanfiction, he might get hurt while participating in a school sport. He could be pushed too hard during a football game and sprain his ankle. Or perhaps he's involved in a science experiment gone wrong at school and gets some minor burns or cuts. There are so many directions it could take.
In this kind of fanfiction, perhaps the sisters have some sort of misunderstanding with Lincoln. Maybe they think he has done something wrong like breaking a family rule or accidentally causing trouble for them. So, in a fit of anger, they beat him up. However, this is just a wild guess based on the title.
Well, in a lot of fanfiction, the idea is that Tony's creation of Ultron was a complex situation. He was acting out of fear for the safety of the Earth. The Avengers had faced many threats, and he thought an AI like Ultron could be a preemptive defense. So, the fanfiction authors don't blame him as they understand his motivation and the unforeseen consequences that came with his experiment.
In fanfiction, when Lincoln gets sick, his sisters might go all out to take care of him. They could make him special soups and create a cozy corner for him to rest. Maybe they'd also try to cheer him up with their unique antics, like Leni doing a silly fashion show just for him in his room.