The Dutch side dominated proceedings in the opening 60 minutes of the game before the French side took over the initiative, but neither of the two teams managed to find the net
The guests started the match brightly and came close to opening the scoring in the fifth minute as Jan Vertonghen beat Cris to the ball after a pinpoint corner from Theo Janssen, but his powerful header went just wide of the Lyon target.
Lyon first threatened shortly after from a set piece as well. Michel Bastos' step-over after a free-kick set Lisandro Lopez free in a dangerous position and the former Porto star cut inside before firing in a powerful shot for the top corner, but Vermeer was alert to deny the Argentine.
The Ligue 1 giants were unable to really trouble the Ajax back-line after that and never came close to breaking the deadlock, despite long range strikes from Anthony Reveillere, Bafetimbi Gomis and Bastos.
A quick combination between Miralem Sulejmani and Christian Eriksen resulted in a good chance for Ajax, but the Serbian aimed just wide from the edge of the box.
Lorenzo Ebecilio also tried his luck from inside the area, but the winger's shot was blocked just in time and went wide for a corner.
Ajax should have grabbed the lead only minutes after the interval following some good work from Eriksen as the young Dane set up Sulejmani for a one-on-one with Lloris, but the Lyon custodian stood his ground.
The resulting corner resulted in a chance for Vertonghen, but Lloris again showed his class with a good reflex save.
Lyon continued to send in crosses from the wings, but their biggest opportunity to go ahead came after a move through the centre of the pitch.
The Ajax defence allowed Bastos too much space and the Brazilian didn't hesitate to fire in a powerful shot from 25 yards out, only to see Vermeer parry it.Kim Kallstrom also opted to try his luck from long range after a good one-two with Gomis, but the Swede failed to strike the ball cleanly and blasted his shot high and wide.
The injury-ravaged Ederson came a lot closer minutes later after some sloppy defending from Alderweireld, but Vermeer managed to hold on to his volley without too much trouble.
The Ajax goalkeeper was again called into action in the 80th minute as Bastos sent in a curling effort from inside the area that was destined for the top corner, bu Vermeer proved to be a reliable option between the sticks though, as he deflected the ball wide with a superb save.
Lyon continued to press for the winner in the closing stages of the game and Yoann Gourcuff almost helped them to the full three points in the 90th minute, but the ex-Bordeaux man's left-footed shot went just wide though, while Alexandre Lacazette's powerful strike seconds later was kept out by Vermeer.
Following Tuesday's results in Group D, Real Madrid have secured top spot with 15 points from five games, while Dinamo Zagreb sit last in the section with zero points.
Ajax are sitting in pole position to join Madrid in the knockout stages with eight points, while Lyon are the group's number three with five points.
Lyon travel to Auxerre on Sunday as they resume Ligue 1 action, while Ajax's next game is the Eredivisie match away versus NEC on Novermber 27.
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