The Eredivisie champions started the match well and created some good chances but can count themselves lucky that the French outfit didn't score a late winner
The hosts started the match with attacking intentions and came close to opening the scoring after five minutes of play. Theo Janssen curled in a superb corner kick for Derk Boerrigter, who beat his marker to the ball before heading only inches wide.
Lyon then showed their class on the counterattack a number of times and Bafetimbi Gomis should have given the Ligue 1 giants the lead in the 17th minute. The forward was left completely unmarked at the far post after a cross from Michel Bastos, but Gomis aimed too high and the chance went begging.
The Frenchman came close again moments later when he went past Jan Vertonghen just inside the Ajax area, but his low shot went wide of the target. Clement Grenier and Bastos both tried their luck from long range as well, but they failed to trouble Kenneth Vermeer between the posts.
Ajax had another big chance to grab the lead in the 37th minute after a fine piece of skill from Kolbeinn Sigthorsson. The Iceland international drifted out wide to lose his marker and sent in an inch-perfect cross for Miralem Sulejmani, but the winger's header from five yards out went just wide.
The guests came out of the dressing room the better side of the two and sloppy defending from Gregory van der Wiel allowed Bastos the chance to go one-on-one with Vermeer. The Ajax goalkeeper denied his opponent with a superb reflex save to keep the match scoreless.
Lyon had another opportunity to break the deadlock in the closing stages of the game after good work from substitute Ishak Belfodil, however, Grenier aimed just wide from 20 yards out. Minutes later, Van der Wiel denied Jimmy Briand with a last ditch tackle as the forward was clean through on goal.
Ajax's next Champions League match is away to Real Madrid on September 27. They resume domestic action on Sunday when they lock horns with PSV.
Lyon take on Dinamo Zagreb at home in their next group game in two weeks time. Their next Ligue 1 clash is the home match against Olympique de Marseille on Sunday.