With Dumbledore, Snape might be more confrontational at first. He could demand answers about all the times he was used as a pawn in Dumbledore's grand plans. But eventually, they would likely come to a new understanding. They were both fighting for the greater good in their own ways, and in the afterlife, they could respect each other's sacrifices more fully.
If he meets Lily in the afterlife, their relationship could become more of a true friendship. Without the complications of James Potter and the war, they could finally understand each other on a deeper level. Snape could let go of his unrequited love and instead cherish the bond of friendship that was always there beneath the surface.
One possibility is that in the afterlife, Snape finally finds peace. He no longer has to hide his true loyalties or endure the scorn of those who misjudged him. He might be reunited with Lily, and they could have the conversations they never had in life. He could also meet with Dumbledore again, and they could discuss all the secrets and sacrifices that were made during the war.
Snape might be portrayed as a more vulnerable character in this fanfiction. Away from the pressures of the wizarding world, he can show his true emotions to Lily.
Their relationship would likely deepen. With no more threats or battles, they can focus on just being friends. They could become even closer as they share their hopes and dreams that were cut short in life.
There could be other Death Eaters that Snape knew in his life. In the afterlife, they might be there to either confront him about his double - agent status or to seek redemption themselves. And sometimes, characters from Snape's childhood, like his parents or childhood friends, might appear to add more depth to his backstory and his experiences in the afterlife.
In romantic relationships in fanfiction, Snape can be quite badass. He might be very guarded at first, not easily giving in to his feelings. But when he does, he's all in. He'll protect his love interest from any danger, whether it's from dark wizards or from the prying eyes and gossiping tongues of Hogwarts. He uses his skills and knowledge to keep them safe, and if anyone tries to come between them, he'll use his wit and magic to drive them away.
One interesting idea could be Snape finally getting the recognition he deserved in the afterlife. Maybe he is reunited with Lily and she thanks him for all he did to protect Harry. Another could be that he gets to teach in a magical afterlife school, sharing his vast knowledge of potions and the Dark Arts.
Their relationship could become more spiritual. Without the physical limitations and distractions of the living world, they can focus solely on their emotional and mental connection. They might be able to communicate with just a thought and understand each other on a deeper level.
Snape's character could become more complex. He might start to incorporate some of Merlin's wisdom into his own actions. For example, Merlin was known for his ability to see the good in people, and Snape could start to do the same. Instead of just being bitter and resentful towards Harry, he could start to see Harry as a potential ally in a greater fight, much like Merlin saw the potential in the young knights of Camelot.
If Snape was an Animagus, it could make his relationship with Harry even more complex. Harry might be initially distrustful of Snape's Animagus form, seeing it as another way for Snape to spy on him. However, as time goes on, he might come to understand that Snape's Animagus ability is also used for other purposes, like protecting Hogwarts in a different way.
At first, it might be tense. Scar was responsible for Mufusa's death, so there would be a lot of negative emotions. But as they interact more, they could start to understand each other better. Scar might show remorse, and Mufusa might show pity or forgiveness.