Victory would put the seven-times French champions second in Group D with one match remaining, away to Dinamo Zagreb, but a score draw or defeat would eliminate them for the first time since the 2002/03 season.
Back-to-back defeats by Real Madrid and a first Ligue 1 home loss in more than a year against Stade Rennes on Friday have dented their self-confidence.
"It will be another competition and sometimes, in the Champions League, we find resources that we do not always have," coach Remi Garde said after his team were beaten 2-1 at home by Rennes.
"We won't have a choice. It's a make-or-break game."
Lyon, who have lost five of their last seven games in all competitions, will have to drastically raise their level if they are to beat Ajax.
"The problem is not our ambition, it's our level of play," said Garde.
Striker Bafetimbi Gomis, who missed several chances against Rennes, reckons he needs to be more lethal in front of goal.
"I should more aggressive, be more like a killer," he said after the Rennes game.
"We have to stop the bleeding. We've already been in this kind of situation and we have what it takes to make it through."
Garde may not be able to field Lisandro Lopez from the start after the Argentine striker made his return from a 12-week injury layoff only as a second-half substitute against Rennes.
Centre-back Dejan Lovren and holding midfielder Maxime Gonalons are expected to be back after shaking off minor injuries.
Ajax travel to Lyon with serious offensive problems as central striker Dmitry Bulykin sustained a knee injury in Saturday's 2-2 draw against NAC Breda.
With Kolbeinn Sigthorsson and Luuk de Jong already out and winger Derk Boerrigter staying at home with back problems, coach Frank de Boer might have to adjust his tactical plans.
The Dutch side are also without defenders Nicolai Boilesen and Andre Ooijer.
Teams (possible):
Olympique Lyon: Hugo Lloris; Anthony Reveillere, Cris, Dejan Lovren, Aly Cisshokho; Maxime Gonalons, Kim Kallstrom, Ederson, Yoann Gourcuff; Jimmy Briand, Bafetimbi Gomis
Ajax Amsterdam: Kenneth Vermeer; Gregory van der Wiel, Toby Alderweireld, Jan Vertonghen, Vurnon Anita; Nicolas Lodeiro, Eyong Enoh, Christian Eriksen, Theo Janssen; Miralem Sulejmani, Lorenzo Ebicilio
