Lily's first kiss was not with James, but with Severus. It was a few weeks before their first year at Hogwarts and it was all they could talk about. Eventually Lily perked up enough courage to express her fear that she would not make any friends, Severus slowly looked up at her and stared right into her eyes and said, "You will always have me." and he kissed her right on the lips quickly, but softly.
Lily got up and left. She was confused, she expected him to comfort her and say that it would all be okay. She never thought of them together. Severus was her friend, sort of. There were days where she would despise him and days that she only got through because of him but she couldn't seem to decide on her actual feelings toward him. She fought over whether or not to continue being friends with him, but she couldn't deny that he was hers. He was always there for her and maybe he did have feelings for her that she didn't share but she needed him and she couldn't let him go, not yet. Eventually she chose to ignore the interaction and act like it never happened. She took a few days before she went back to their normal spot where she was sure he was and she acted like herself and made sure not to bring up the kiss or feelings, she kept it completely platonic. Eventually the event bothered her less and less. Lily convinced herself it never really happened, maybe it was just a dream or a nightmare, she couldn't decide. But James never knew, he was always under the impression that he had given Lily her first kiss and she went to the grave believing that herself.
Severus on the other hand had a goofy smile on his face the rest of the day. He sat in bed that night thinking of the possibilities of the next day. He only thought of good scenarios, so when Lily did not show up at their usual spot the following day he was confused. Over the next few days he started doubting his actions and hating himself for doing what he did. He was sure she hated him. He ruined the only friendship he'd ever had. He thought that it was the perfect thing to do in the moment, but after four days and no sign of Lily he was no longer sure. When she finally showed up on the fifth day he was sure she was going to yell at him and end the friendship, but she didn't. She didn't say anything about the kiss and neither did he. Somedays he would wonder if it actual happened or if it was all just a perfect moment he created in his head? So they went back to normal and Severus realized that this was how they would always be. Friends and nothing more.
When they went to Hogwarts nothing more than friends slowly became less and less until it was just nothing. Deep down they both knew the end started those few weeks before going to Hogwarts but neither was ever brave enough to confront the other and the relationship dwindled into nothing.