One possible consequence is that he could lose the trust of his friends. If everyone believes he is responsible for something his sister did, his friends might start to distance themselves from him.
Well, in such a fanfiction, Naruto might become a scapegoat because of false accusations. Maybe his sister gets into some trouble and Naruto is wrongly blamed for it. For example, if there is an incident in the village and the sister is involved but tries to shift the blame to Naruto for some reason like jealousy or self - protection.
Well, there could be several consequences. Firstly, it could damage the author's reputation within the Naruto fan base. Since the idea is so against the norms of the series, other fans might see the author as someone who doesn't understand or respect the essence of Naruto. Secondly, it might be flagged or removed from fanfiction platforms due to its inappropriate nature. And thirdly, it could start unproductive and negative debates within the fan community, which can create a hostile environment for everyone involved.
One possible consequence could be a change in his fighting style. Without his eye, he might have to rely more on his other senses like hearing and smell, similar to how blind ninja in the Naruto universe adapt. For example, he could focus more on using his chakra to sense the movements of his opponents.
Naruto might also go through an identity crisis. His whole life has been centered around being a ninja with chakra and using powerful jutsu. Losing his chakra could make him question who he is and what his purpose is. He would have to redefine himself and find a new way to contribute to the ninja world. This could be a long and difficult process for him.
One possible consequence is that he might become more powerful. With his dark emotions out of the way, he could focus better on his training and unlock new abilities. Another consequence could be that he becomes more isolated. Since his dark emotions were a part of what made him relatable to others, without them, he might seem distant.
Naruto might end up feeling extremely lonely. His family has always been an important part of his life. Without their support and presence, he could become depressed or start making even more reckless decisions. Also, if his family tries to search for him, they could get into danger themselves in the process, which would be an unintended consequence of his hiding.
One possible consequence is that he gains new and extremely powerful abilities. With the Rinnegan, he could have enhanced perception, be able to use all six paths techniques more effectively, and perhaps even have the power to manipulate time and space to a certain extent. This would make him an even more formidable opponent.
One possible reason could be to protect her. Naruto might believe that by leaving, he can draw danger away from his sister. For example, if there are powerful enemies targeting him, he doesn't want his sister to get caught in the crossfire.
One consequence could be a loss of self - confidence. His heritage has been a part of what has motivated him to become stronger. Without that connection, he may start to doubt his abilities.
One possible plotline could be that Lemon has some unique ninja abilities that Naruto discovers, and they train together to become stronger. Maybe she has a special chakra nature that Naruto has never seen before, and they figure out how to use it in combat.