What makes jily an interesting/compelling ship for you? What do you think attracted lily to james and vice versa?
I think James had a crush on Lily from early on. And a big part of it, I think, was that she was willing to stand up to him. James, pre-Hogwarts, seems to have been rather spoiled and sheltered. And at school, he was apparently popular in Gryffindor. Lily was someone he liked and understood to be a good person, but who wasn't so easily impressed by him. I think that presented a challenge that made her more appealing to him.
Lily, I think, truly disliked James at first, or at least disapproved of his behavior. Up until that behavior started to change. I think that towards the end of their time at Hogwarts, the situation going on outside was becoming more serious, and the Marauders grew up a lot. All of a sudden they weren't just schoolyard bullies or trouble makers anymore, they were starting to take a stand for something that mattered. Lily was always inclined to see the good in people (see also: Snape), and I think the idea of the reformed bad boy would actually be very appealing to her. Not in an "I can change him!" kind of way but in the sense of being impressed to see him change for the better on his own, and willing to reconsider her previous opinion of him.
And then, taking a closer look, I think she would find someone who is a very loyal friend. Which is something I think she would value, given her own bad experience with a broken friendship. As well as someone who despises blood status prejudice despite it working in his favor, and wants nothing to do with the Dark Arts. On some level, they share similar values, even though their backgrounds and personalities are very different.
And then, of course, there's the fact that they were Head Boy and Head Girl. Which obviously doesn't automatically lead to romance, but in their case I think it helped. Because now they're a team. They have to work together. And as they do, sparks fly.
I like that she challenges him and pushes him to grow as a person without being made responsible for fixing him or being portrayed as a prize for him to earn. I like that she learns to see a different side to him that was always there on some level, but isn't obvious to her at first. I like the almost but not quite enemies to lovers type of situation.
And, honestly, I kind of love that it's a tragedy, too. Because I'm a sucker for good angst, and Jily certainly has that.