Celtic are bottom of their UEFA Champions League qualifying group after defeats in their opening two matches against AC Milan and Barcelona.
Ajax have one point against their name following a 1-1 draw against Milan in Amsterdam and Lennon insists anything less than a victory would leave the Hoops on the brink of elimination.
"Put it this way, tomorrow is a must-not-lose game as I am confident with this team that we can perform away from home as well," he told Sky Sports News.
"Winning the game would put us in a really good position within the group but losing would probably end our aspirations for trying to qualify.
"I watched Ajax on Saturday night (drew 1-1 at Twente) and they came on very strong in the second half and probably deserved to take something out of the game.
"They are going to give us problems the way they move the ball about, the way they play the game. They have pace in their team in wide areas but we're ready.
"And we're looking forward to it. We know what's at stake and the fact that we are at home gives us a slight edge."
And Lennon is confident Kris Commons will be back in his starting line-up for the return in Amsterdam early next month after a hamstring injury ruled him out of Tuesday's match.
"He's been for a scan and we're waiting on confirmation but he is feeling a lot better now," he said.
Commons will be joined on the sidelines by Scott Brown (suspended), Adam Matthews (shoulder) and Derk Boerrigter (ankle) but Emilio Izaguirre has recovered from illness and should start while Mikael Lustig will undergo a late check on his hip injury.
"Both Mikael and Emilio trained today," said Lennon. "Emilio will be fine and we'll assess Mika tomorrow. We're pretty hopeful he'll be fit.
"Joe Ledley only played 20 minutes on Saturday after a month out so it's debatable whether he'd be able to do the 90 minutes against Ajax."
Watch Celtic take on Ajax at Parkhead from 7.30pm on Tuesday, live on Sky Sports 3.