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.
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.
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.
She might meet her father, Harry Potter, when he was still a student at Hogwarts. This would be an amazing encounter as she could see a side of her father she never knew before.
A possible fanfiction could involve Lily Luna Potter and her time - traveling adventures. She accidentally stumbles upon a time - turning device and gets sent back to the time of the first Wizarding War. There, she has to be careful not to disrupt the timeline while also trying to learn from the events of that time to prevent a similar future catastrophe.
One common plot line is her struggle with identity. She's a Potter but in Slytherin, so she has to figure out where she belongs. Another is her proving herself in Slytherin, showing that she can be just as great as any other Slytherin. For example, she might excel in Potions, which is a Slytherin - associated subject.
Well, it really depends on the fanfiction author's creativity. Some might give her a Patronus that reflects her own unique personality traits. For example, if she's portrayed as very brave and fierce in a particular fanfic, her Patronus could be a lioness, representing her courage and leadership. Another possibility is that it could be a bird, perhaps a phoenix, which would tie in with the magical and powerful nature often associated with the Potter family.
There's a fanfiction that focuses on Lily Luna Potter's relationship with her family's legacy. She feels the pressure of being a Potter but also embraces it. In this story, she has to prove herself worthy of the Potter name in a magical competition held at Hogwarts. It's a story about self - discovery and living up to one's family's reputation.
There are many fanfictions that feature Lily Luna Potter. Some might focus on her life at Hogwarts. For example, she could be in a situation where she has to deal with a new dark threat that is emerging. In this fanfiction, she might form an unlikely alliance with students from different houses to combat this threat, and through this experience, she grows as a witch and as a person.
There could also be fanfictions that focus on Lily Luna Potter's family life. How does she interact with her parents, Harry and Ginny? What about her relationship with her siblings? Fanfiction might explore her growing up in a post - Voldemort wizarding world, dealing with the expectations that come with being the daughter of the famous Harry Potter.