Well, it could be that in the fanfic, Naruto is exposed to a new teacher or a different fighting culture that uses the lean fighting style. This new style might attract him because it has some similarities to his own ninja style, like the importance of balance and quick reflexes. He could then start to blend the lean fighting style's unique footwork and body positioning into his regular fighting techniques, creating a whole new and exciting combat approach.
In fanfic, Naruto might be made to use the lean fighting style in several ways. Maybe he could incorporate its quick, evasive maneuvers into his ninja combat. For example, the lean fighting style's emphasis on using the body's momentum to dodge attacks could be adapted by Naruto, who is already very agile as a ninja. He could use it to quickly shift his body weight and avoid enemy jutsu or physical strikes.
The lean fighting style in a Naruto fanfic could be a result of a plot device where Naruto has to learn a different way of fighting to overcome a powerful enemy. The lean fighting style, with its focus on fluid movement and efficient energy use, might be just what he needs. He could learn to lean in and out of attacks, using his chakra in a more controlled way, similar to how the lean fighting style uses physical energy. This would not only make his fighting more diverse but also more unpredictable for his opponents.