Well, in some fanfics, Naruto might use his shadow clones to create a distraction and then slip away. Maybe he's on a mission he deems more important than staying in the hospital.
Tsunade for sure. As the Hokage and also a medical expert, she would be furious about Naruto escaping the hospital. She might send some ninjas to bring him back.
The setting also plays a big role in such a fanfic. If the story is set in a time when Root is under more scrutiny from the village leaders, it might be easier for the OC to escape. For instance, if there are political tensions and Root is trying to keep a low profile, the OC could take advantage of the chaos. Also, the OC's knowledge of the Root's hideouts and routines would be essential for a successful escape. They might have memorized the patrol schedules or known the secret passages within the Root's base.
In some 'OC escapes root Naruto fanfic', the OC might be a long - hidden spy within Root who decides to escape when they discover the true, often dark, intentions of the organization. They could use their inside knowledge of Root's operations and bases to plan their escape route carefully. This often leads to a series of intense chase scenes and battles against Root operatives as they try to make their way to safety and perhaps ally with the main Naruto characters.
I'm not entirely sure specifically as there could be many different interpretations of a 'naruto hospital lemon fanfic'. It might involve a story set in the Naruto universe within a hospital setting, perhaps with some original or unique plotlines created by the fanfic author.
In the fanfic, Naruto might be in the hospital because of some strange illness that no one has seen before. The doctors in the hospital are trying all kinds of methods to cure him, and he might be feeling really frustrated lying in the bed all day. He could be thinking about all the things he wants to do once he gets better, like going on new missions or training harder.
Well, of course, the original character (OC) is a main focus. This OC is often a unique individual with skills or a backstory that sets them apart. Then there are usually some representatives from the Root organization. They act as the antagonists trying to stop the OC from escaping. And sometimes, main Naruto characters like Naruto himself, Sasuke, or Kakashi might make an appearance, either helping the OC or being involved in the events related to the escape in some way.
Obviously, Naruto could be one of the main characters. He could be either a patient or someone helping out at the hospital. Another main character could be Sakura. Since she has medical skills, she could be a doctor or a medic - ninja in charge at the hospital. And then there could be a new character, like a young orphan who is being trained as a medic - ninja at the hospital and has an interesting backstory.
One possible plot could be a story where Naruto gets seriously injured during a battle and is taken to the hospital. There, he meets a young and talented medic - ninja who has a unique healing ability. As he recovers, they form a bond and the medic - ninja helps Naruto discover a new way to control his chakra, which in turn helps him become stronger.