At first, it would become very strained. Harry might avoid Lupin at all costs. He would no longer trust Lupin and would be suspicious of his every move.
As the story progresses, it could either get worse or start to heal. If the truth behind the reason for Harry's hatred is gradually revealed, there could be a chance for reconciliation. However, if more misunderstandings pile up, the relationship could become irreparable. Lupin, on his part, would probably be very confused and hurt by Harry's sudden hatred, which could also affect his own actions towards Harry.
One possible event could be that Lupin lied to Harry about something important. In the world of Harry Potter, trust is a huge factor. If Lupin deceived Harry, it could easily turn Harry against him. Say, Lupin lied about his whereabouts during a crucial time when something bad happened, and Harry suspected Lupin's involvement.
One possible reason could be a misunderstanding. Maybe Lupin did something that Harry misinterpreted as betrayal or negligence. For example, if Lupin was forced to keep a secret from Harry for his own safety, but Harry found out in a way that made him feel deceived.
Maybe in that fanfic, Lupin did something that Harry considered a betrayal. For example, he might have made a decision that put Harry or his friends in danger without consulting them first.
One great 'Harry Potter - Arsene Lupin' fanfic is 'Lupin's Legacy'. It delves deep into Lupin's past and his relationship with the other characters. It shows how his werewolf nature affected his life at Hogwarts and beyond in a really interesting way.
In many such fanfictions, Harry might start off with a basic admiration for Lupin as his teacher. But as the story progresses, he could come to see Lupin as a true father figure. Maybe Lupin shows him kindness and understanding that Harry lacks from other adults in his life. This could make Harry's view of Lupin deepen from simple respect to a more profound emotional connection.
Character development makes it interesting. In a good fanfic, Lupin's complex character is explored further. His struggle with his werewolf identity, his loyalty to his friends, and his role as a teacher all can be delved into more deeply than in the original books.
Lupin might use his own experience as a werewolf to relate to Harry. He could teach Harry how to control his thirst for blood, much like he controls his lycanthropy. For example, by using potions or certain meditation techniques.
I'm not entirely sure as I haven't read this specific fanfic. But generally, a fanfic with Lupin and Harry might involve some sort of adventure or relationship exploration within the context of the Harry Potter universe. However, the 'spanks' part is a bit strange and might not follow the typical positive themes of the original series.
In Harry Potter, Sirius and Lupin did not raise Harry. Harry had been brought up by his aunt and uncle, and Dumbledore had done so for two main reasons: to prevent Harry from being infected by fame and fortune too early, and to prevent Voldemort or his henchmen from finding him. Although Sirius and Lupin were close friends of Harry's father, James, and played an important role in protecting and guiding Harry as he grew up, they did not take responsibility for raising Harry. Harry Potter and the Order of the Phoenix is not enough. Please click to read the novel!
They could go on a mission to find a rare magical creature that is important for some reason. Maybe it has a power that can help defeat the dark forces. Or they might travel to a hidden magical place that Lupin once knew about from his own adventures as a young wizard. There, they face various challenges and have to use their combined knowledge of magic to get out safely.