The lie concerns the history of firefighters. Montag's interest in this subject is prompted by his first encounter with Clarisse. At first, she is scared, due to his occupation. As they talk, she grows more comfortable.
They walked still further and the girl said, "Is it true that long ago firemen put fires out instead of going to start them?"
"No. Houses have always been fireproof, take my word for it."
"Strange. I heard once that a long time ago houses used to burn by accident and they needed firemen to stop the flames."
So at this point, Montag firmly believes that firemen have always started fires, & that houses have always been fireproof. It's a clear example of the misinformation and re-writing of history that the government in the novel perpetrates. Yet something sticks with Montag, and he brings it up to Beatty later.
Montag hesitated, "Was-was it always like this? The firehouse, our work? I mean, well, once upon a time..."
"Once upon a time!" Beatty said. "What kind of talk is THAT?"
Fool, thought Montag to himself, you'll give it away. At the last fire, a book of fairy tales, he'd glanced at a single line. "I mean," he said, "in the old days, before homes were completely fireproofed " Suddenly it seemed a much younger voice was speaking for him. He opened his mouth and it was Clarisse McClellan saying, "Didn't firemen prevent fires rather than stoke them up and get them going?"
"That's rich!" Stoneman and Black drew forth their rulebooks, which also contained brief histories of the Firemen of America, and laid them out where Montag, though long familiar with them, might read:
"Established, 1790, to burn English-influenced books in the Colonies. First Fireman: Benjamin Franklin."
So Beatty doesn't directly answer Montag's question, but by letting the other men pull out their rulebooks, he implies that their version of history is correct. This, of course, is a lie.