Perspective
Disclaimer: I do not own Harry Potter. Thank you for your time.
If anyone were to ask her what she thought about James Potter, she would immediately reply with her standard answer, "He's an annoying toe rag." Usually because of the vehemence of her words (and perhaps the terrifying look on her face) she would be left alone after that, but there were the small few who would dare to question her choice of words. In that situation, she would merely choose to walk away until the other person came to their senses.
Truthfully, she feels that her description encompasses his character completely.
He was a show off in class, on the Quidditch pitch, and even in the Great Hall – although how someone can show off at eating is something Lily still does not understand. It just wasn't possible for his accomplishments to go unnoticed and especially not when he had the awful habit of dedicating each one to the "beautiful witch with the flaming red hair". Lily supposed that she ought to think herself as lucky, how many other girls would James Potter name (and later mistakenly make out with) a Quaffle for?
He was also a great, big bully that often picked on the Slytherins for ridiculous reasons such as the way they deemed to walk – "They were walking past me funny, Evans! What was I supposed to do, die and leave you to Snivellus?"
If there are any qualities to a toe rag, Lily thought , it would have to be their arrogance and their cruelty.
Perhaps those same qualities could explain why he was annoying, but Lily felt there was another reason altogether to this trait – James Potter was annoying because of the things that he chose not to show off.
He was annoying because of the work that he truly did put in for the things that he wanted to achieve, but work that he chose not to announce as an accomplishment. Sometimes, Lily thinks that she wouldn't mind receiving a dedication for that.
He was annoying because of the way he treated people when he was too tired to bully, often helping them with their Transfiguration homework and even allowing them to practice the spells on him when they were too afraid. The most annoying part of that is how his friends, the people who know him better than anyone else, treat these occurrences as if they were common and normal, not the rare glimpses Lily searches for.
He was annoying because of the way he would often make humorous and witty jokes that made Lily want to laugh despite her company. He was annoying because of how happy seeing her struggle to contain herself made him.
He was annoying because of the way he let his emotions control him, often causing him to do stupid and (admittedly) heroic things. He was annoying because as cruel as he could be, he knows the difference between right and wrong and his decisions always seem to be things he truly believes in.
No, Lily knew that if there was any way at all to describe the intricacies of James Potter – of the boy she'd known since first year, and even the man he was now becoming in their fifth year – it would only suffice to say that he was an annoying toe rag.
As much fun as it is to read about irrational Lilys who just hate James Potter to their very core and see no good in him at all, I think that since Remus describes Lily as someone who "saw the good and beauty in everyone" then she must have seen some good qualities in him even when she didn't like him very much.