Maybe it's a member of a long - lost ninja clan. This clan member could have some special skills and knowledge that they want to pass on to Naruto. They choose to train him in secret to protect their clan's secrets from falling into the wrong hands.
There's a possibility that it's a spirit or a ghost of a great ninja from the past. This entity might have chosen Naruto because of his strong will and determination. Since it's a spirit, it has to train Naruto in secret as its existence might not be acceptable in the ninja world or might attract unwanted attention from dark forces.
Perhaps a fallen god who, despite losing his status, still has the knowledge of how to train a God of Destruction. This character could have his own motives for training Naruto, like regaining his former glory through Naruto's success.
Well, it could be about Naruto finding a hidden master who teaches him unique jutsus in secrecy. Maybe this master has a special connection to an ancient ninja clan and imparts knowledge that no one else in the village knows.
It could be an unknown ninja from a far - off village who specializes in Storm Release. This ninja might have heard of Naruto's potential and decided to train him.
It could be an old, retired ninja who lives on the outskirts of the village. This person has seen the hardships Naruto faces and decides to take him under their wing.
There's a possibility that his trainer is a self - taught expert. This person could have learned about pistols through years of exploration and practice. They see potential in Harry and take it upon themselves to train him, sharing their unique and unorthodox methods of pistol training with Harry.
It could lead to Naruto developing much stronger abilities earlier and having a different path of growth.
In this fanfic, Lilith could be an original character created by the author. She might be a powerful and mysterious figure with special abilities that make her suitable to train Naruto.
It could lead to Naruto becoming even stronger and more skilled than in the original story. Jiraiya's training methods might unlock new powers for him.
She could be someone with a special bloodline or ability. Maybe she has a unique form of chakra that gives her certain powers. In the context of training Naruto, her skills and knowledge are what make her important. She could be a mysterious figure who has been observing Naruto for a while and decides to take him under her wing to help him reach his full potential. For instance, she might have the ability to see the latent potential in others and wants to shape Naruto into a great ninja not just for his own sake, but also for the greater good of the ninja world.
Kosuke might be a character created specifically for this fanfic. He could be someone with a unique background, like perhaps he was once a disciple of a great ninja but then went on his own path. And now he sees potential in Naruto and decides to train him. He could have abilities that are different from the main characters in the original Naruto series, which is why he has something new to offer to Naruto in terms of training.