There could be several motives. Firstly, some writers might want to create a high - impact, thought - provoking story. By having Harry's parents kill him, they immediately draw the reader's attention and make them question everything they know about the 'Harry Potter' world. Secondly, it could be an exploration of the nature of good and evil. Even the most 'good' characters in the original series, like Harry's parents, could be made 'evil' in this fanfiction. It might also be a way to show how fragile the concept of heroism is. If Harry, who was destined to be a hero, can be killed by his own parents, it makes the idea of heroism more complex and less straightforward.
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 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.
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 misinformation. If Harry is fed false information about Sirius being a traitor or a danger, he might act on it. For instance, if a well - disguised Death Eater manages to convince Harry that Sirius has joined Voldemort, Harry, in his haste to protect others, could attack Sirius.
Mental illness could be a motive. For example, schizophrenia might make her have hallucinations or delusions that her parents were a threat.
One possible motive could be extreme revenge. After years of being mistreated, locked in a cupboard, and generally being made to feel unwanted, Harry might snap in fanfiction. Another could be a sense of self - preservation if the Dursleys were somehow involved in a plot against Harry's life in the fan - created plot.
Lucius may also have a moment of moral awakening. Despite his past actions, he could see the value in Harry's life and the good that he represents. Maybe he has a change of heart after seeing the destruction caused by Voldemort's actions and decides to do the right thing for once by saving Harry.
In a fanfiction, Dumbledore might steal out of desperation. Suppose there was a situation where a curse was about to be unleashed on Hogwarts, and the only way to stop it was by stealing a particular ingredient for an antidote from a place where it was not supposed to be taken. Dumbledore, seeing no other option, decides to steal it. His motive here is to save the school and its students, even if it means breaking the rules.
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 a misunderstanding. Maybe Snape is framed for something really bad, like a dark magic plot against Hogwarts. Harry, in his haste to protect the school and his friends, believes Snape is guilty and takes drastic action. Another reason could be if Snape accidentally endangers someone Harry loves dearly, like Ginny or Ron, and Harry's emotions get the better of him in the heat of the moment.
One possible motive could be that the 'mountain' in the fanfiction represents a great evil or obstacle that is threatening the wizarding world. Harry, being the hero, feels it's his duty to eliminate it. For example, if the mountain is a lair for dark creatures that are attacking Hogwarts students.