One common theme is redemption. Lily might be seen as redeeming herself for leaving Harry so early in his life. Another theme is the power of love. Their meeting often showcases the strong bond of love between a mother and son. And the theme of second chances also pops up a lot, as if the meeting is a second chance for both of them to have a relationship.
Perhaps Sirius Black could also be involved. Sirius was Harry's godfather and was very much a part of Harry's life. His presence could add some interesting dynamics, like he could be the one who stumbles upon the magic that makes the meeting possible and then has to deal with the implications of Harry meeting his mother.
Maybe in the fanfiction, Harry accidentally enters a parallel dimension where Lily is still alive. Here, Lily discovers that Harry is her future son. She might take him under her wing and train him in a different way of magic, one that was perhaps forgotten in Harry's own time. This could lead to Harry having unique powers and a different approach to dealing with the Dark Arts and his enemies.
It could be a dark wizard who is jealous of the bond between Harry and Lily. This wizard might try to break their connection and use Lily's power for his own evil purposes. Maybe he wants to control Lily's magic, which is known to be strong, to achieve domination over the wizarding world.
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.
One popular 'lily meets harry fanfiction' might be 'A Mother's Love'. It delves into the emotional reunion of Lily and Harry in an alternate universe. Another could be 'Lily's Return', which focuses on how their meeting changes the course of Harry's life in Hogwarts. There's also 'Unexpected Encounter' that shows a very different side of their relationship when they meet.
A really good 'Harry meets James and Lily' fanfiction is 'Time - Twisted'. It starts with Harry being pulled into a time - rift during a battle. When he meets James and Lily, the story explores their personalities in great detail. You can see James' cocky charm and Lily's kind yet strong - willed nature as they interact with Harry. Another one is 'The Past Beckons'. It's a more heart - warming story where Harry is given the opportunity to spend a day with his parents. He learns a lot about their past and their hopes for him. And 'Reuniting with the Past' is also a great read, with a focus on how the meeting changes Harry's perspective on his family and his own identity.
One interesting plot could be that Harry meets Lily in a time - traveling scenario. He gets to have a conversation with his mother, learning things about his family that he never knew before.
A great fanfiction in this regard is 'When Potters Meet'. Here, James and Lily are brought back to life briefly and they cross paths with Ginny. The story focuses on Ginny's reaction to meeting the parents of the man she loves. It shows her respect and admiration for them, and there are some really sweet moments where they exchange memories and advice about Harry.
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.