Adorable! Is this a one-shot? I hope not!!!
The first two paragraphs of your story are my favorite. I love the way you paralleled Lily and James's opinions and thoughts of each other, using the rest of the story as the catalyst of their relationship. I really liked the line "...if he gave up now, then he would never have anything to do with her. So he would continue to ask her, and thrive off what little she gave in return;" I think you captured James's character wonderfully in that sentence. In those few words you justified his annoying persistence with his growing desperation that he would never have any sort of relationship with Lily. You also did a wonderful job hinting at Lily's relenting in the first paragraph (while describing her judgements of James)--I liked how you let little bits of her soft-spot for him seep through.
I did notice that some of the grammar and capitalization was off. For example, the sentence "Perhaps he would finally realised [...]" doesn't read well. Transfiguration and Quidditch should be capitalized, always. In James's speech to Lily, some of his words sound more American than British, even to my Americanized ears ("wanna", "sorta", etc.). I also think that the transition between the second and the third paragraph could have been a little smoother.
Lastly, I like your subtlety in the last two paragraphs with hinting at the death of Lily's parent(s). I think you did a very fine job expressing how she had come to rely on James, that he was now the one she turned to for comfort. I'm glad you didn't end it with a snog, but you still managed to show that their relationship had progressed from the friendship James had promised her. Throughout this entire story, you focused the mental chemistry between them instead of the physical, and you pulled it off very well. Great job!
I liked this story. It was short, sweet, and simple. Good job for your first story!