Well, often she's shown as having to deal with a lot of prejudice. People assume she's going to be like the 'typical' Slytherin, but she's not. Her character in fanfiction can be written as being more independent. She doesn't just follow the crowd. For example, she might form her own group of friends from different houses, using her Slytherin cunning to bring them together. And she could also be more in - touch with the darker aspects of magic, not in an evil way, but in a way that she wants to understand it better to use it for good.
In some fanfictions, Lily Luna Potter in Slytherin might be portrayed as an outcast within her own family's legacy. Since the Potters are mostly associated with Gryffindor, her being in Slytherin could make her feel like she has to prove herself more. She might be depicted as having a more cunning side, using her Slytherin traits to achieve her goals while still maintaining some of the Potter family's good - heartedness.
Many fanfictions portray Lily Luna Potter as a very friendly and inclusive character. She is likely to have friends from all the houses in Hogwarts. This is because she values the unity among witches and wizards, and she believes that everyone has something unique to offer, regardless of their house affiliation. So she is often seen as a unifying force within the Hogwarts community.
She would likely become more resourceful. In Slytherin, she'd be surrounded by those who know how to use their surroundings to their advantage. So, Lily Luna might learn to be more cunning in getting what she wants, while still holding onto her moral compass from her family. For example, she could find clever ways to study for exams or solve mysteries around Hogwarts.
Writers may also differ in how they show the characters' relationships with their peers. One writer could have Lily Luna being extremely popular among her classmates, while her brothers are more of the loner types. Another might write that all three of them are part of a tight - knit group of friends, but each has a different role within the group. Lily Luna could be the mediator, one brother the joker, and the other the responsible one.
A living Lily in fanfiction might be depicted with a different personality. In the original story, we mainly see her through memories, but in fanfiction, she can be given new traits. She could be more assertive or more involved in political aspects of the wizarding world. For instance, she might take a stand on issues like blood purity in a more direct way than she could in the original plot, which was cut short by her death.
The family can be shown as constantly hovering around Lily Luna. For example, they could always be checking on her whereabouts, like sending magical tracking spells on her without her knowledge. They might also be very strict about who she can be friends with, forbidding her to associate with certain wizarding families that they think are 'bad influence'.
Well, it could be portrayed as a very emotional encounter. Lily Luna, being curious and kind - hearted, would approach Petunia with an open mind. Petunia, though, might be guarded at first. Maybe the setting could be at Petunia's old home, and Lily Luna would be nervous but determined to make a connection. The fanfiction could focus on their body language, like Petunia folding her arms defensively while Lily Luna tries to smile reassuringly.
Perhaps she forms an unlikely friendship with a pure - blood Slytherin who has very traditional views. Lily Luna tries to show this friend a different perspective on blood purity and the wizarding world in general. Their friendship causes a stir in the Slytherin common room, but they stick together through it all.
Their relationship could be portrayed uniquely by having Snape be a mentor to Lily Luna Potter in the art of Occlumency. Since he was a master of it, he could pass on his skills to her. This would create a bond based on trust and the sharing of secrets. Lily Luna Potter, in turn, could show Snape a new perspective on life in the post - Voldemort wizarding world, something he never got to experience fully.
Often, she's portrayed as highly intelligent. Slytherins are known for their brains, and a female Slytherin in fanfic might be top of her class in subjects like Potions or Ancient Runes. Her intelligence gives her an edge in the complex world of Hogwarts, where knowledge is power.
When Harry is in Slytherin in fanfiction, his view of the wizarding world may change. He may start to see the grey areas more clearly. Instead of seeing things as simply good or bad, he realizes that there are many factors at play. This makes him more complex as a character. He may also have to deal with the Slytherin legacy of the Dark Arts. He has to navigate through the temptations and warnings related to it. He might study some Dark Arts spells not to use them for evil, but to understand how to defend against them, which is a very different path from what he would have taken in Gryffindor.