One way is to show their relationship through shared memories. Since Harry has access to some of his mother's memories through magic, they could be explored in a way that deepens their connection. For example, Harry could relive his mother's first kiss and understand more about her as a person.
A unique way to show their relationship is to have Harry Potter enter a magical realm where he can have conversations with his mother as if she were still alive. In this realm, they could talk about things like his future, his father, and how she feels about the wizarding world as it is now. This would allow for a very deep and emotional exploration of their relationship.
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.
The relationship could develop uniquely if Fem Harry Potter uses her empathy skills. Since she is different from the original Harry, she might be more in tune with Bellatrix's pain and past traumas. For example, if she discovers that Bellatrix was once a victim of dark magic herself which led her to become a Death Eater, Fem Harry Potter could try to heal her. This would create a very different dynamic compared to the usual enmity between Harry and Bellatrix.
If Lavender was cursed in some way that made her forget her memories of Hogwarts, Harry could be the one to help her regain them. He would take her around the castle, showing her familiar places and telling her stories of their time together. As she slowly starts to remember, she begins to see Harry in a new light. This process of rediscovery could lead to a deep and emotional connection between them, as they are basically rebuilding their relationship from scratch. And it would also show Harry's caring side towards someone who wasn't necessarily in his inner circle before.
In the fanfiction, their relationship could be developed uniquely if Fem Harry Potter is from a different magical culture. James Potter is intrigued by her different ways of using magic and her cultural beliefs. They start to exchange knowledge and through this, a relationship blossoms. James helps her adapt to the Hogwarts way of life while she broadens his perspective on magic in general, and they become very close as a result.
Their relationship could be portrayed uniquely by having Snape be a mentor to Lily Luna Potter in the art of Occlumency. Since he was a master of it, he could pass on his skills to her. This would create a bond based on trust and the sharing of secrets. Lily Luna Potter, in turn, could show Snape a new perspective on life in the post - Voldemort wizarding world, something he never got to experience fully.
In a fanfic, their relationship could be developed through a magical project. Suppose the Ministry wants to create a new protective charm for the whole wizarding world. Harry Potter, with his unique experiences and skills, is invited to be part of the project. As they collaborate, they learn about each other's strengths and weaknesses. The Minister might be initially dismissive of Harry's unorthodox methods, but as they see the results, they start to trust and rely on each other more.
In a fanfic, the encounter between Harry Potter and Death could be shown in a more philosophical way. Death could be portrayed as a wise being, not menacing but rather calm. Harry and Death might sit down, like in a dream - like landscape, and have a long conversation about life, death, love, and sacrifice. The scene could be filled with soft light and a gentle breeze, symbolizing the peaceful nature of the discussion despite its heavy topic.
It could develop as Harry teaches Lily Luna advanced magic. He might start with Patronus magic, and as he guides her through the process, they get to know each other better. Lily Luna, in turn, could share her school experiences with Harry, and they start to understand each other on a deeper level. They might also have some father - daughter disagreements, which they work through, further deepening their relationship.
You could have a love potion that works differently than the traditional ones. Instead of making someone fall in love instantly, it could make them see the best in the person they are attracted to. So, for example, if Ginny uses this new - type of love potion on Harry, he starts seeing all her heroic deeds and noble qualities more clearly, which deepens his love for her in a more meaningful way.
Their relationship could develop through a shared love of a particular magical creature. For example, they both discover a new, endangered magical creature and have to work together to protect it. This shared mission could bring them closer.