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 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.
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 if his brother was somehow a threat to the village. Naruto is very loyal to Konoha, so if his brother was planning to destroy it or harm its people, Naruto might feel compelled to stop him at all costs.
Well, it could be for the sake of exploring a different kind of magic or a different set of rules in the wizarding world. Perhaps in this fanfiction's version, the parents were under some sort of dark magic influence that made them turn on Harry. Or it could be a psychological exploration. The writer might be interested in delving into the minds of Harry's parents and seeing what could make them do such a heinous act. It could also be just a very different take on the concept of family and love in the 'Harry Potter' universe.
One possible motive could be power - related. Sasuke might see Naruto as a symbol of something he wants to control, maybe Naruto's power or his unwavering spirit. By making Naruto his pet, he could feel a sense of superiority.
It could be due to severe mental illness or untreated psychological disorders that led him to commit such a horrifying act.
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 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 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.
Well, it could be a dark corruption of power. Maybe in this fanfic, the 'god' power Naruto obtains warps his mind. He might see his family as a threat to his new - found godly status, fearing they'd try to stop him from using his power in certain ways.