What kind of relations between Lily Potter and Lucius could be explored in fanfiction?

Yes, there might be some fanfictions exploring their relation. In the Harry Potter universe, Lily Potter is from the side of the good, and Lucius Malfoy is on the 'dark' side. Fanfictions could create various scenarios of how they might be related, perhaps through some convoluted family ties in the wizarding world's complex history, or through some magical events that bring them into an unexpected connection.

The relationship can be explored by having Lily Luna Potter look up to Harry Potter as a hero. She could constantly seek his advice on her studies at Hogwarts or her own magical adventures. For example, when she has trouble with a difficult spell, she turns to her father for help.

One possible relation is that the Queen is a patron of the wizarding world in the fanfiction. She could be secretly funding Hogwarts or other magical institutions. This would create a connection between her and Harry Potter as he is part of the wizarding world that she is supporting.

They could have adventures exploring different realms of heaven. Maybe there are places full of magical creatures they've never seen before. They might be on a quest to find a special kind of magic that can help Harry in some way, even from the afterlife.

A possible scenario in this love triangle fanfiction could be that Lucius, after his fall from grace in the wizarding society, tries to redeem himself in a way that involves getting close to Hermione. Draco, on the other hand, has always had a sort of love - hate relationship with Hermione. As Hermione gets involved with both of them in different ways, like helping Lucius with his redemption and having academic or magical adventures with Draco, she finds herself in the middle of a confusing love triangle. Her feelings for both of them would be a mix of attraction, pity, and admiration, which would make for a very interesting fanfiction story.

One possible plot could be that Harry, for some reason, has to take on the role of a healer for Lucius. Maybe Lucius gets seriously injured during a battle or some dark magic backfires on him. Harry, with his knowledge of magic and his good heart, decides to help Lucius despite their past differences. This could lead to a series of interactions where they both learn more about each other and perhaps even form an unlikely alliance.

Maybe Lucius wants to use Harry for his own gain. Harry is a famous figure in the wizarding world, and Lucius could be thinking of leveraging Harry's status for something, like getting back into the good graces of the wizarding society after his fall from grace.

There could be. Fanfiction often explores alternative universes and relationships. But this concept goes against the canonical story where Harry is James and Lily's son. In fanfiction, authors can play with these ideas freely, but it may be controversial among some fans who prefer to stick to the original storylines.

Well, perhaps Lily Potter discovers a magical time - traveling device. She could end up in a future where Hogwarts has changed drastically. Maybe there are new spells and magical creatures that she has to adapt to. And she might meet her descendants or future versions of her friends.

One reason could be for the greater good of the wizarding world. If Lucius is healed, he might be able to turn away from the Dark side and provide useful information about Voldemort's remaining followers.