This short scene begins in the middle of a chapter I call Lupin's Secret. I seriously do think that J.K. Rowling has something going on between Sirius and Lupin. This is my take on how the revelation of their relationship might actually surface.
LUPIN'S SECRET
..."Don't you ever think about what he is doing?" Harry asked cautiously.
Lupin continued writing and replied without looking at Harry.
"I prefer not to dwell on it. Things are very serious in the living world and that is what I must commit myself to now." He put down his quill to look up at Harry through gray strands of hair and mustered a smile.
"All right Harry?"
"NO!" he screamed. Harry slammed his fists on the table, thoroughly startling Lupin. For to long people had been asking Harry if he were all right and expecting him to say Yes. Even when they knew he was grieving everyone wanted to hear Yes. Harry was sick to his stomach of all the people who expected him to accept things without any explanation.
"It isn't all right anymore!" Harry roared.
"Harry, just calm down. You know there's nothing—"
"Nothing anyone can do, right? What's wrong with you! You could have done something! You were right there! You held me back and you were the first one to say that he was dead!"
Harry paused for breath but broke into another outburst before Lupin could defend himself. He kept a steady gaze on Harry.
"Why didn't you try to save him? He was your friend! Didn't you care about him? DIDN'T YOU GIVE A DAMN!"
At Harry's last words Lupin sprang from his chair so quickly that it hit the floor.
"Of course I gave a damn," Lupin said icily. "And he was more than my friend! I loved Sirius." Lupin took in a deep, unsteady breath. He took up his quill and parchment then returned his gaze to Harry.
To Harry, Lupin's face looked sadder, older and lonelier than ever he had seen. Stunned and speechless by Lupin's confession Harry regretted his words silently.
"I'm sorry to have put this on you, Harry. I believe you're old enough to handle the news. Sirius and I meant very much to each other."
Harry nodded slowly and lowered himself into a chair.
"Now, I'll be turning in. Have something to eat and then be off to bed. You can't be missing your train tomorrow." Lupin left the kitchen not looking ashamed of the information he had unexpectedly divulged to Harry. His footsteps paused at the place—Harry guessed—where Sirius' painting hung. After that he was left alone with his own thoughts. Harry realized that others were suffering from Sirius' death, possibly even more than he was.
Harry lay his head in his hands and stayed there for a good while, wondering what to do with himself.