There could be a fanfic with this title, but the use of 'lemon' makes it a bit suspect. In the world of fanfiction, there are so many different takes on Naruto and Hinata's relationship. But if it's a 'lemon' fanfic, it's likely to contain adult - themed content. So, if you're looking for proper, non - inappropriate fanfics about them, you should look for ones that are rated for general audiences.
If it exists and is appropriate, perhaps it could be about Naruto accidentally doing something that upsets Hinata, like breaking a promise or a precious item of hers. And then he has to go through a journey of making it up to her, with their relationship evolving in the process.
There's no way to really know for sure if it's popular without looking at the relevant fanfic platforms' statistics. It might be popular within a small niche of Naruto fans who are interested in this particular type of story about Naruto and Ino. But considering the potentially controversial 'lemon' part, it may not have a broad popularity across all Naruto fanfic readers.
He might become really withdrawn. Naruto is a very emotional person, so if Hinata breaks his heart, he could isolate himself from his friends and the village. He would probably be too hurt to face them.
Since I haven't actually read this specific 'naruto breaks ino lemon fanfic', it's hard to say precisely. It could potentially be about Naruto disrupting Ino's plans or routine in the context of the Naruto universe. Maybe Naruto's actions break Ino's expectations or the status quo in their relationship, be it as friends, rivals or something else.
One characteristic is the focus on the relationship between Hinata and Naruto. These fanfics often explore their emotional connection in depth. For example, they might show how Hinata's shyness and Naruto's boldness interact.
It could be that Hinata publicly humiliates Naruto. She might expose some of his deepest insecurities in front of the whole village. Since Naruto has always been striving for the village's acceptance, this betrayal from Hinata, who he loves, would be a huge blow to his heart.
In a fanfic, there could be a mystery in Konoha where strange things are happening around the lemon groves. Naruto, Hinata, and Sakura are assigned to investigate. As they dig deeper, they discover that an old enemy is using the lemon groves as a cover for their evil plan. Naruto uses his strength, Hinata her Byakugan, and Sakura her intelligence to solve the mystery and save the village.
One common theme could be self - discovery. Hinata might break away from her normal path to find out more about herself. Another theme could be independence, where she stands on her own without relying on Naruto or her clan.
Naruto could be initially in shock. Given his strong feelings for Hinata, he might not believe it at first. He could try to talk to her and ask for reasons, hoping to fix things.