Character development is crucial. The OC should be well - defined with unique traits and a believable backstory. Their relationship with Lily should be developed gradually, like in a real - life relationship. For example, in some good fanfics, the OC starts as a friend or a study partner of Lily.
The integration into the Harry Potter universe is important. It should feel like the OC and their relationship with Lily fit seamlessly into the world of Hogwarts, magic, and the existing characters. The fanfiction should also respect the established lore of the Harry Potter series. For instance, not changing the fundamental rules of magic just for the sake of the story.
A good plot is necessary. It could be about the OC and Lily facing a common threat together, or it could be a story about how the OC helps Lily discover something new about herself or the wizarding world. This keeps the readers interested and engaged in the story as the relationship between the OC and Lily evolves within the plot.