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.
In the fanfiction, it could be that he gets into a fight with someone who doesn't like him and gets punched in the face, leaving him with a black eye and a swollen lip.
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.
The shooter could be a main character. We could explore their motives, their background, and what led them to commit such a heinous act. For example, if the shooter was a disgruntled former soldier who felt Lincoln had wronged him in some way. Another character could be Lincoln's wife. We could see her reaction, her grief, and how she copes with the situation. Or perhaps a doctor who tries desperately to save Lincoln's life could be a main character, showing the medical challenges and the hope against all odds.
One common theme could be family support. Even when Lincoln is hurt, his large family might come together to help him through. Another could be his struggle to overcome the situation that's causing him harm, whether it's emotional or physical.
His sisters could be main characters. For instance, Lori might give him some advice on how to deal with the braces since she's the eldest and has more experience. Or Leni could be there to offer some fashion tips to make him feel better about his new look with the braces.
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.
Physical hurt might come from a powerful magic spell. Let's say an evil sorcerer casts a spell that drains Yami's energy and causes him pain. His struggle to overcome this and regain his strength could be a central part of the fanfiction.