Jonathan Bamba curled in a fine 20-yard strike to give Lille the lead but Zeki Celik's own goal just before half-time brought Lyon level.
The visitors played most of the second half a man down after Brazilian defender Marcelo was shown a second yellow card for a foul on Bamba but Lille could not take advantage.
"The first yellow was very harsh," said Lyon coach Rudi Garcia.
"Quite frankly, it killed the match. I would like to have seen 95 minutes against Lille with 11 against 11. I'm not going to say what I think... I'm very annoyed because it became difficult afterwards."
Lille stayed second but fell two points back of PSG while Lyon moved up to sixth after a fifth draw in nine outings this term.
Bamba notched his fourth goal of the campaign with a terrific first-time effort after an inviting lay-off from Turkey international Burak Yilmaz.
The goal came moments after Mike Maignan stood tall at the other end to deny Karl Toko Ekambi after the Cameroon striker was played clean through.
Lyon goalkeeper Anthony Lopes pawed away a long-range shot from Yilmaz and Bamba then fizzed just over, but OL equalised when Houssem Aouar's drive smacked Celik in the chest and flew past Maignan.
The dismissal of Marcelo five minutes into the second half prompted Garcia to withdraw Aouar for centre-back Djamel Benlamri, the Algerian Africa Cup of Nations winner who joined Lyon last month on a free transfer.
Lille were unable to transform their sustained pressure into a winning goal and were held to a second consecutive draw.
Volland up and running
Earlier, Germany international Kevin Volland scored his first goals for Monaco since signing for the club in September as Niko Kovac's side thrashed Bordeaux 4-0.
Monaco struck three times in as many minutes through Wissam Ben Yedder, Gelson Martins and Volland in the first half to take control at the Stade Louis II.
Volland then grabbed another in the second half as Monaco won for just the second time in six matches to climb up to eighth place.
France forward Ben Yedder crashed home a spot-kick on 27 minutes after his header was handled by Pablo, with a penalty awarded despite the ball looping over Benoit Costil and into the net following the deflection.
Martins grabbed his first goal since serving a six-month ban for pushing a referee last season when he lunged at the far post to poke in a Ruben Aguilar cross.
And former Bayer Leverkusen forward Volland promptly headed in from a Ben Yedder delivery to end his drought following his 11 million-euro ($13 million) move from Germany.
The 28-year-old tapped in a second on 57 minutes as Martins slid the ball across goal for his unmarked team-mate.
Nice moved up to fourth as Patrick Vieira's team extended their unbeaten domestic run to five games with a 3-0 victory at Angers.
Rony Lopes put Nice ahead on 11 minutes and Pierre Lees-Melou added a second from the spot. Hicham Boudaoui came off the bench to net a third as Nice stayed four points behind PSG.
Metz continued their fine recent form with a 1-0 win at Nimes while Montpellier defeated Saint-Etienne by the same scoreline courtesy of a goal from Englishman Stephy Mavididi.
Reims beat Strasbourg 2-1 while Dijon remain the only team without a victory following a goalless draw at home to Lorient.
Standout matches today