Well, it could be that Naruto has to learn how to interact with monster classmates. Maybe he discovers new jutsus that are unique to the monster world in school.
There could be such a fanfic, but finding it might be difficult. Fanfic communities are huge and diverse, but the term 'lemon' usually implies some sort of adult or sexual content, which may not be allowed in all fanfic platforms. Naruto is a very popular franchise, and the idea of a 'King of Monsters' crossover is interesting, but it doesn't guarantee the existence of a lemon - themed fanfic.
In the 'Naruto goes to the North' fanfic, he may come across a group of nomadic ninjas. These ninjas have a different way of life compared to the ones in Konoha. They might be more in tune with nature and have unique abilities related to the natural elements of the North. Naruto could learn a great deal from them and they could also be potential allies in his adventures in the North.
There could be a mysterious new student in the fanfic. This new student might have some secrets of their own and befriend Percy. They could be from a different place or have some special powers or knowledge. Additionally, there might be some school janitors or cafeteria workers who play small but important roles in Percy's school experiences, like giving him some good advice or helping him out in a difficult situation.
Well, in a 'Percy Goes to School Fanfic', Percy might face some bully problems at school. Maybe there are some mean kids who pick on him because he's different.
Well, it could be about Naruto arriving at Hogwarts and being confused by all the magic there. Maybe he tries to use his ninja skills in a world full of wizards and witches.
In a 'naruto goes berserk fanfic', Naruto might lose control of his chakra in a new and extreme way. Maybe he's pushed to the edge by a powerful enemy that he can't defeat with his normal strength.
One possible plot could be that Naruto is pushed over the edge by the constant betrayal he faces. For example, if the village he has always protected turns against him due to false accusations of being a threat. He might start using his powers in a more erratic and dangerous way, not caring about the consequences. This could lead to a showdown between him and his former friends who now see him as a menace.
Naruto and Hinata's date could start with Naruto being a bit nervous. He picks Hinata up at her place. They go to a local park. Naruto tries to show off a little by doing some cool ninja moves on the trees. Hinata blushes and tells him how amazing he is. Then they sit on a bench and share some dango. Naruto listens intently as Hinata talks about her day at the hospital. It's a simple but sweet date.