Well, they might first be a bit confused when they meet. Hermione, being from a different time, would have different ways of doing magic and speaking. But soon, they could find common ground. Maybe they start by comparing their experiences at Hogwarts. Hermione could tell Lily about the new spells she has learned, and Lily could share some of the old, forgotten magic with Hermione.
Well, in the 'Lily meets James parents fanfiction', there could be a lot of interesting scenarios. For instance, James' family might have some unique traditions that Lily has to adapt to. There could be some awkward moments at first, like when Lily accidentally spills something during dinner. However, through James' support and her own charm, she gradually wins over his parents. They might end up sharing stories about James as a child, which brings Lily closer to them.
In this fanfiction, perhaps Snape finally gets the chance to truly apologize to Lily. He might express all the unspoken feelings and regrets he had when she was alive.
Perhaps in the 'hermione meets the lestranges fanfiction', Hermione stumbles upon the Lestranges while on a secret mission. She might initially be at a disadvantage, but then she could use her knowledge of magic and her quick thinking to turn the tables. For example, she could use some of the spells she learned from the library that the Lestranges are not familiar with. And she might also try to appeal to any shred of humanity left in them, if there is any, to get what she wants or to avoid getting harmed.
In such a fanfiction, Hermione's encounter with the Dursleys could be full of drama. Since Hermione is a clever witch, she may use her magic knowledge to expose the Dursleys' ill - treatment of Harry. For example, she could magically make Dudley see how wrong his parents' actions are. At the same time, she may also try to bridge the gap between the wizarding world and the Dursleys, though it would be a difficult task considering the Dursleys' deep - rooted dislike for anything magical. However, Hermione's determination might bring some unexpected changes to the Dursleys' household.
One possible scenario in a 'Hermione meets Lily' fanfiction could be that Hermione uses a time - turning device and accidentally ends up in the past where she meets Lily. Maybe they bond over their intelligence and love for books. Hermione could be in awe of Lily's kindness and bravery, and Lily might be intrigued by Hermione's knowledge of magic from the future.
Well, it could be that Lily Luna Potter meets the past versions of her famous friends or relatives. She may interact with them in ways that change the course of events she knew from history, creating all sorts of interesting twists. For example, she could give some advice to a younger version of someone that has a big impact on their future actions.
Well, in this fanfiction, perhaps Lily Luna Potter might be shocked by the Dursleys' cold and unfriendly attitude at first. She could be confused as to why her family has such strange relations. Maybe she tries to show them the magic world's beauty in an attempt to change their views on magic and wizards.
In this fanfiction, perhaps James would be extremely nervous when he meets Lily's parents. He might try to make a great first impression by bringing a bouquet of flowers or some small gifts. Maybe he stumbles over his words while trying to introduce himself, but his sincere love for Lily shines through and eventually wins over her parents.
In such a fanfiction, Hermione might initially be in great danger. The Death Eater could try to capture her to use as leverage against Harry Potter. Maybe she uses her quick wits and vast magical knowledge to outsmart the Death Eater at first encounter.
One possibility is that Ginny, being a big fan of Harry's stories about his parents, would be in awe of Lily. She might ask Lily all about her time at Hogwarts, her relationship with James, and her experiences with the Marauders. Lily could be impressed by Ginny's courage and skill in Quidditch, seeing a bit of herself in the younger witch.