Lemoine started and finished a fine team move in the 82nd minute, slotting past goalkeeper Rudy Riou after running onto Ricky Van Wolfswinkel's pass.
Ivory Coast winger Max-Alain Gradel missed a good chance to make it 2-0 shortly after.
Two-time defending champion Paris Saint-Germain played seven-time champion Lyon later Sunday.
Earlier, Lille missed the chance to leapfrog Marseille at the top after failing to break Montpellier's defense in a goalless draw, and sits one point behind the top three in fourth place.
Lille was the more dangerous side but could not find the target as Montpellier, sitting back in its own half, kept the hosts at bay.
Marseille's 3-0 win against Rennes on Saturday put it level on points with Bordeaux but with a better goal difference. The top three all have 13 points after six rounds.
Marcos Lopes, Michael Frey and Jonathan Delaplace combined well in the 24th minute for Lille, only for the latter to miss his strike. Montpellier goalkeeper Geoffrey Jourdren was forced into a good save soon after to deny Ryan Mendes' effort and Lopes failed to score from the rebound.
Montpellier improved after Romain Sanson came off the bench in the second half but Rolland Courbis' side struggled to move the ball forward.
"We had a miserable start to the game and we were fortunate enough not to concede in the first half," Montpellier winger Anthony Mounier said. "Leaving Lille with one point is obviously a good result as I can't see many teams sharing the points here."
Montpellier, which won the title ahead of Paris Saint-Germain two years ago under current Lille boss Rene Girard, moved up to fourth, three points behind Marseille.
Elsewhere, Monaco followed up its 1-0 victory over Bayer Leverkusen in the Champions League midweek with a 1-0 win against Guingamp to climb out of the relegation zone.
After goalkeeper Jonas Lossl had saved Joao Moutinho's free kick, winger Nabil Dirar pounced to fire home in the 38th.