Lewis allowed a cross-cum-shot from substitute David Hutton to squirm under his body after 66 minutes. It was the on-loan Tottenham youngster's first goal for the basement boys, and he had only been on the pitch for four minutes.
Victory would have sent Darren Ferguson's men to the summit and all appeared to be going to plan when Aaron McLean broke the deadlock nine minutes before the interval.
McLean, who had earlier seen a shot rebound off both posts and be denied by a smart Scott Brown save, lashed home from six yards after a Craig Mackail-Smith delivery had fallen into his path.
But Posh were guilty of squandering chances to extend their lead before the costly Lewis error. Another first-half effort from McLean was well saved before Andy Lindegaard blocked Mackail-Smith's follow-up on the line.
Then in the second period a Paul Coutts drive bounced agonisingly wide after clattering of Mackail-Smith. Despite the draw, Posh are still odds-on for promotion and Cheltenham remain 12 points from safety with only five matches remaining.