Both sides wasted good chances to earn victory with Lyon going close late on when Yoann Gourcuff's shot shaved the post.
Ajax are second in Group D on eight points, three ahead of the French side going into the final round of matches. They have an identical head to head record but the Dutch side have a far superior goal difference.
Former European champions Ajax need only one point at home against group winners Real Madrid to reach the last 16, while Lyon will look for a huge win at Dinamo Zagreb and hope Ajax lose.
"We were up against a good Ajax side, and it cost us a lot of energy just to dispossess them," Lyon coach Remi Garde told French TV channel TF1.
"We lacked sharpness in front of goal.
"I still believe we can go through but it will obviously be complicated."
The home side face the prospect of not making it through the group stage for the first time since the 2002/03 season.
Lyon began brightly with returning forward Lisandro Lopez, making his first start in 12 weeks after an injury layoff, having his curling shot parried away by Kenneth Vermeer in the seventh minute.
Lyon could not build on their good start and Ajax midfielder Christian Eriksen was a constant threat although the visitors failed to create clear-cut chances in a dull first half.
Ajax looked sharper after the re-start and it took a timely save by Hugo Lloris to deny Miralem Sulejmani after he had been fed a through ball by Eriksen.
Sulejmani's deflected shot on the hour just cleared the crossbar before Lyon got going again after Brazilian midfielder Ederson replaced Lisandro with 20 minutes left.
Ederson had a volley blocked by Vermeer as Lyon desperately pushed for the winner, and the seven-time French champions went close again when Michel Bastos's angled shot was tipped away by the Ajax keeper.
Lyon had penalty claims turned down with two minutes left when Ederson appeared to be brought down and then Gourcuff's shot shaved Vermeer's left post.
