You could start with a simple scenario, like one of them attending the other's concert. Then build on that. Think about their personalities. Lana Del Rey seems more laid - back and mysterious, while Marina is very energetic and confident. Incorporate these traits into how your characters interact. You can also research their real - life interviews and public appearances to get more ideas about how they might act in different situations.
First, listen to a lot of their music. Get a feel for their lyrics, melodies, and the emotions they convey. This will help you capture their essence in your writing. For example, Lana Del Rey often has a dreamy, nostalgic feel to her music, while Marina and the Diamonds has a more flamboyant and edgy style.
Begin by creating a setting. It could be a modern - day city like Los Angeles or London. Then introduce your characters. Maybe Lana Del Rey is walking down the street and bumps into Marina and the Diamonds. From there, let their conversation flow naturally. You can add elements of drama or humor, depending on what kind of fan fiction you want to write. Remember to stay true to their overall images as artists while also adding your own creative twists.