Don't question the logistics of how and when Luna happened to exist within Grimmauld Place when Sirius was alive, just go with the flow, you'll enjoy it more.
Luna drifted in to the kitchen quite unexpectedly, making Sirius and Remus break off from their conversation as the passing of her slender, pale figure took them by surprise. Remus, of course, had already met Luna, and simply smiled at her as she threw them a glance with her glowing, orb like eyes. Sirius was so used to having strangers walk in to his home like they owned the place these days that he barely batted an eyelid, but even he realised that there was something eerily different about this strange girl, and so he gave Remus a questioning look.
"Who's that?" He mouthed as Luna turned her back to pour herself some pumpkin juice from the flagon on the kitchen counter top.
Remus shook his head to show that he would tell Sirius later. But at that moment Luna turned, and did the introducing for him, "I'm Luna Lovegood. I've met you before, Professor Lupin, but I don't believe that we have ever met," She told Sirius, her tone light and casual, like they were discussing the weather, "I know who you are though."
"Of course you do. I'm the murdering lunatic who broke out of Azkaban to try and kill you all," Sirius said dryly. Remus frowned at his friend, wishing he could be a bit politer.
"I did think that at first," Luna agreed, nodding thoughtfully, "But Harry speaks very highly of you, the whole Order does, really."
Sirius cocked his head to the side. "You're Xenophilius Lovegood's daughter, aren't you?" He asked Luna.
Luna nodded serenely. She turned her attention to the werewolf now instead. "How are you, Professor?" She said.
"Please, Luna, call me Remus. I don't teach you anymore, after all," Remus said kindly, "I am... quite well. And yourself?"
"Exceptionally fine," Luna said with a smile that only made her look more unhinged.
Sirius chuckled softly to himself. He decided that he liked this girl. "What brings you to my humble abode, Luna?" He enquired.
"My father thinks I'll be safe here," Luna said, frowning as though this troubled her a bit.
"No where is safe anymore," Sirius muttered.
"Sirius, don't frighten her!" Remus cried.
"I'm not frightened," Luna explain softly, "In fact I agree. This house for instance, it's really not as safe as it appears to be."
"And why is that?" Sirius said, "Kreacher might look like he has a death wish for everyone in the place, but he's harmless really. Just give him a good kick, that usually gets rid of him."
Remus sighed as if he had lost the will to live when it came to his best friend.
"Kreacher is lovely," Luna said, "A little bitter maybe, but lovely all the same. But this house, it's full of Knargles. And something else I forgot the name of... Excuse me, but I must write to daddy to find out what they're called."
Luna made her way towards the door. "It was nice seeing you again, Luna," Remus called to her.
"Yes, you too, Professor," Luna said, then she turned and inclined her head to Sirius, "It was a pleasure to meet you, Mr Boardman."
She skipped off down the hall, her glass of pumpkin juice sloshing as she went. Sirius and Remus exchanged puzzled looks. "Who the hell is Mr Boardman?" Sirius muttered.
He had obviously never read the Quibbler.