I'm taking a bit of creative licensing with this because I know not everything in the Marauders lives is completely clear. In "Harry Potter and the Prisoner of Azkaban" the movie Remus mentions Lily's being there at a time for him when no one else was. I tried to think of when that would be. I remembered the incident when Sirius tried to trick Snape into coming to the Shrieking Shack and almost got him killed. I imagined that Remus probably got very angry about that because they were kind of exploiting his illness to get a laugh. I thought perhaps if this time cause a sever in their friendship, it would be the time when Lily would be there. Now there has been some confusion and speculation as to when this incident happened. One that makes the most sense to me is that the incident happened a few days before the "Snape's Worst Memory" incident. Then, at the "Snape's Worst Memory" incident, I believe that Remus was back to normal and on good terms with the other Marauders.
My apologies for any off canon pieces or grammatical or spelling errors
Disclaimer: The credit belongs to the brilliant J.K. Rowling.
A Glass of Pumpkin Juice
"Looks like a lovely day outside," Sirius stared out the window of his dormitory. He yawned as he fumbled through a drawer of wrinkled, half-folded shirts. "I'm thinking we should get some breakfast, then er…take a day off from History of Magic." Peter excitedly nodded. He always agreed with Sirius. "Sound good?" Peter again nodded.
"Yeah," James sat up in his bed, ruffling his already messy hair. "Sounds good to me," he was carefully eyeing Remus who seemed to be ignoring Sirius' suggestion as he buttoned up his uniform.
"What about you Remus?" Sirius asked. Remus again ignored him, grabbing a Transfiguration textbook and leaving the dormitory. Sirius hurried after him, followed by Peter. "Remus," he called after him and Remus descended the staircase to the common room answering back with an annoyed, "Leave me alone." "Remus, c'mon," he called again, but, by that time, Remus had made his way out of the portrait hole. Sirius stood frustrated. James appeared from the dormitory. "You've just got to let him cool off," he told Sirius. "We really got him angry." Sirius, dejected, nodded his head and went back into the dormitory. Peter, copying his expression, did the same.
Lily Evans was particularly good at multitasking, but drinking her pumpkin juice, studying for Charms, and keeping an eye on Severus Snape was not an easy task. She and Snape had been friends since before they attended school, but, recently, he was worrying her. He was running with the wrong crowd and seemed to be enjoying it. Just the day before, Lily was scolding him on his involvement with such revolting boys as Mulciber and Avery, whom Lily detested. She desperately wished she could go back to the day of her and Snape's sorting and change the outcome—have him sorted into Gryffindor with her. Then maybe he'd be acting a bit better. Although she didn't like to admit it, Lily knew that Snape probably would have ended up in the same position. He'd had a troubled childhood and always seemed far too interested in Slytherin and the dark arts. Despite their differences, Lily still tried to remain his friend, but his companionship with Avery and Mulciber and involvement in some of their downright evil escapades was putting a terrible strain on their friendship. She had to finally say something. Their talk ended on good terms. Lily hoped that maybe Snape would start to change. Although that hope lingered, she watched him intently, anticipating the arrival of his wretched Slytherin friends. So far, he ate alone. Lily kept telling herself to study, but she couldn't stop watching him. She'd read over the same sentence in her Charms book at least four times. He was studying a ratty old Potions book, excitedly scribbling in it every few minutes. Every once in a while he would look up to grab a bit of food. This time his head stayed up for a few minutes. He seemed to be looking at someone. Although his sullen expression rarely changed, he seemed to gain a look of even more disgust. Noticing his expression, Lily turned her head in the direction he was staring to find Remus Lupin looking back him, seemingly embarrassed, scared, or sad. Lily couldn't really tell. Remus didn't often carry the same smirk that his best friends James and Sirius did. After a few seconds of the shared glance, Remus bent his head and found himself a seat at the breakfast table taking a glass of pumpkin juice and nothing else. Lily turned away from Snape and changed her attention to Remus. Remus was a nice boy, studious, friendly, a prefect. Lily and he would often discuss teachers and classes. Once they'd spent an entire afternoon talking about an essay for History of Magic. They weren't what one would call the best of friends, but they were definitely friendly. Remus would reciprocate Lily's hellos and smiles in the corridors even when he was with his friends, who took more enjoyment out of irritating Lily than just about anything else. Remus was the only link, or the only link Lily would like to admit, between Lily and his friends, the school's infamous Marauders, James Potter, Sirius Black, and Peter Pettigrew. The only time Lily tolerated them was when Remus would speak to her. Although Remus was a nice boy, that didn't exempt him from all the mischievous ways of the Marauders. He was often found with them playing pranks, skipping class, or wandering around the castle at night. At least once a month the Marauders would disappear for an entire evening. Many reports put them near the Whomping Willow, possibly the most dangerous tree growing on the grounds. Apparently, the Headmaster, Albus Dumbledore, had planted it during the previous summer. Why Lily couldn't even guess. Snape had taken the matter into his own hands a few nights before and apparently, somehow, James Potter saved his life due to guilt or loss of nerve, Lily didn't know which. Lily didn't know all the details. It seemed like Snape wanted to tell her, but never revealed everything. The only thing he kept emphasizing was that James, Sirius, and Peter snuck out by the tree and the whole thing was Sirius' fault. Lily could never guess why he didn't mention Remus. Remus didn't treat Snape as awfully as James and Sirius, but he certainly never stopped them. Lily wondered if maybe if Remus was out that night. Remus was a strange boy. Ever since first year, Remus disappeared about once a month. At first no one, not even Lily, noticed. Remus was smart, but never really made his presence known in class. However, after a few months, people started taking notice. The generally accepted rumor was that he had some sort of serious or contagious illness that became its worst once a month. Snape had his own theories, but Lily always tried to brush them off. Now, however, seeing Remus and Snape lock eyes, like Snape knew something, made her curious. What was even stranger than Remus' strange illness was that for the past few days, weirdly coinciding with the time Snape went to the Whomping Willow, Remus hadn't been speaking to James, Sirius, or Peter. He paid full attention in class, taking notes and participating rather than talk to them, he generally ate alone or mixed himself in a miscellaneous group of Gryffindors, he went to bed earlier, hardly responded to them when they called and outright refused to say anything when called Moony, the Marauders' nickname for him. In fact, Lily swore that for the past few days, the Marauders had stopped calling him Moony.
Lily continued to watch Remus. He only took about two sips of pumpkin juice before getting up from the table, somewhat irritated, and heading for the door. It only took Lily a few seconds to realize why. James, Sirius, and Peter had just entered the Great Hall. As Remus passed them, Peter attempted to say something, but James stopped him. The three found seat at the end of the breakfast table and helped themselves to only a few pieces of toast—definitely not the large, obnoxious breakfast they normally ate. Lily normally didn't like to involve herself in people's business without being asked or permission, but she couldn't take it anymore. She grabbed a new glass of pumpkin juice and headed out the door as well.
Lily found Remus exactly where she though he would be sitting against the walls of the castle, quietly reading. She hesitated, trying to convince herself to approach him. Remus is a good friend. He would want her to be concerned about him. She approached not wanting to disturb him. He looked up just when she was inches from him. "Morning," she sat next down. He closed his book, "Good morning?" "Trouble in paradise?" she asked offering the glass of pumpkin juice, "I thought you might like this," she smiled handing him the glass of pumpkin juice. "I saw you didn't finish yours." He hesitantly accepted the glass managing a small smile. "I saw you at breakfast," she admitted referring to his ignoring of the other Marauders, "and yesterday. I know James and Sirius are gits, but I didn't think they could do anything to upset you this much." Lily had a point. James and Sirius could be very arrogant and obnoxious, but Remus always looked past those flaws. They had always been the best of friends to him. He always thought they deserved to be forgiven, but, as of a few days ago, Remus had had enough. "They just…" he stared off into the sky for a few moments as if he was trying to find the right words. He had nice eyes, especially when the sun hit them just right—a blue grey. Lily preferred hazel, but his were definitely pretty. "They just don't understand some things," he looked at her and laughed again. It was nice to see Remus laugh. He normally held a calm expression—not sad, unless it was around the time of his disappearances, but not overwhelming happy. "I can imagine it must be difficult," Lily replied trying to show her sympathy. This caught Remus off guard. "What?" Lily realized her mistake in presuming that Remus knew that people had theories about his disappearances. "You know," she hoped he would just let it go, but he continued to stare, "everything, James, and Sirius and all. What are you studying?" she nodded towards the book. "Oh, Transfiguration," Remus answered, and then proceeded by surveying the ground. "Oh." She scanned the grounds for a few moments trying to think of more superficial questions, but nothing came to mind. "Remus," she turned to face him directly. "I just want you to know, I'm not saying that Sirius, James, and Peter aren't good friends to you. I mean I think you can do much better, but, anyway," she tried not to ramble. "I just wanted to say if you someone to talk to, I want you to know I'm here," she smiled standing up and brushing the grass off her uniform. "See you at lunch?" Remus looked up and smiled, "I'll be right here." As she walked back into the castle, Lily contemplated whether that was an invitation or not. She decided that it must have been and planned on meeting him at that very spot at lunch.