One possible motive could be jealousy. Maybe the sister is jealous of Naruto's popularity, his strength, or the attention he gets from others in the village.
One possible motive could be a major misunderstanding. Maybe Naruto was under some kind of mind - control or false information that made him believe the Uchiha clan was a threat to the village on a much greater scale than they actually were. So, in an attempt to protect the village, he took extreme action.
One possible motive could be revenge. Another character might have a grudge against Lucy for something she did in the fictional world, like betraying a group or stealing something precious.
One possible motive could be jealousy. Maybe she was jealous of Naruto's growing power and popularity within the village. Another reason might be related to some dark family secret or a curse that forces her to take his life against her will.
The sense of isolation could be a motive. If Naruto never truly felt accepted in Konoha despite his efforts, he might snap. He's always wanted to be recognized, but if that never fully happens, he could turn on the village. For example, if he's constantly passed over for important missions or not given the respect he thinks he deserves as a powerful ninja.
One possible motive could be jealousy. If Kiba were to gain more recognition in the village than Naruto in the fanfiction world, Naruto's insecurities could drive him to do something drastic like killing Kiba. But this is a huge departure from his usual self.
Another possible motive is that Orochimaru sees Naruto as a potential powerful ally or tool. Naruto has shown great potential and growth throughout the series. Orochimaru could think that by taking Naruto and molding him in his own way, he could have a powerful weapon at his disposal. He might also want to use Naruto to get back at Konoha in some way, since Naruto is one of Konoha's most important assets.
If such a fanfiction exists, perhaps the motive could be a misdirected attempt at protecting the greater good. Maybe Dumbledore thought Hermione's parents were in some way a threat to the wizarding world's secrets that he was trying so hard to protect. But this is still a very far - fetched idea as Dumbledore was always about protecting life in the official story.
One possible motive could be that Dumbledore saw a future where Harry's parents' deaths were necessary for a greater good. Maybe he knew that Harry would be the only one to defeat Voldemort in the end, and their deaths were a catalyst to set Harry on that path.
One possible motive could be a misunderstanding. Maybe Naruto was tricked into believing that Sasuke's sister was an immediate threat to the village. Another could be that she was somehow involved in a dark plot against Naruto's friends, and Naruto felt he had no other choice to protect them.
One possible motive could be a complete breakdown of the peace they had worked so hard to build. Maybe an outside force manipulates Gaara's mind, causing him to turn on Naruto. Another could be extreme jealousy over Naruto's popularity or power.