One common theme is family love. Since they are family, many fanfictions explore the deep love between Lily, James and Harry. Another theme is sacrifice. Given James and Lily's sacrifice for Harry, it's often explored further in these stories. For example, how their sacrifice influenced Harry's character and actions.
One possible fanfiction could focus on the moments leading up to their death. It might show James trying to protect Lily and Harry until the very last moment. He could be shown using his wand to fend off Voldemort as long as he could, while Lily was huddled in a corner with baby Harry, praying for a miracle.
Well, it could lead to a very different story. Harry's childhood and upbringing would be completely changed, and the dynamics of the wizarding world might shift.
Harry would often be a main character in these fanfictions. Since it's about bashing his parents, his reaction and how he copes with the new view of them is a big part of the story. Another could be Sirius Black. He was very close to James, so fanfictions might explore his feelings towards the bashing of his best friend.
Love is a very common theme. It shows how James and Lily's love developed, from their initial meeting to falling deeply in love. Another theme is sacrifice, like how they were willing to sacrifice themselves for Harry. And family is also important, as they were about to start their own family when tragedy struck.
One of the main themes is loss. With Lily leaving James, there's a sense of something being broken in Harry's family. It's about how Harry deals with that void in his life.
One great fanfiction could be 'Lily and James: A Love Beyond'. It delves deep into their relationship before Harry was born. It shows how they met at Hogwarts, their initial dislike which gradually turned into love. The story also includes their adventures as members of the Order of the Phoenix and how they fought against the Dark forces side by side.
If James and Lily survive, it's likely that Harry's training and development as a wizard would be very different. They might have a greater influence on his magical education and his understanding of the wizarding world's politics and history.
One of the main characters often featured is probably Sirius Black. Since he was so closely associated with James, he can be a key figure in these fanfictions, either trying to defend James' reputation or being forced to face the new, negative view of his friend. Another character could be Severus Snape. Given his complex relationship with both James and Lily, he can play a major role in these stories, perhaps finally getting the 'upper hand' over James in some bashed - version scenarios.
Well, 'The Adventures of Harry, Lily and James' is a great read. It takes the characters on fictional adventures that they might have had. It shows James' protective side towards Lily and Harry in a really engaging way. Also, 'A Glimpse into the Potter Family' gives a nice look at their family life, with details about how they interacted on a daily basis and how their relationships grew.