The Scottish champions collected their first Group H win a fortnight ago with a 2-1 win over the Dutch giants at Parkhead, raising expectations for the return at the Amsterdam ArenA.
A victory over Ajax could take Celtic to second in the group ahead of Milan, depending on how the Italian side fare against leaders Barca.
But Lennon has tried to play down expectations, and insisted his side need to be at their very best to avoid leaving the Netherlands empty handed.
"We always knew that the double-header against Ajax would be pivotal and it has proved to be the case," he said.
"You don't know what is round the corner but what I would say is that on their day Ajax are as good as Barcelona and Milan.
"They caused us as many problems as both those teams and I think it will be the same on Wednesday night.
"I think it was important that we got some points on the board against Ajax. But we are under no illusions as to how difficult this will be.
"Ajax were very unfortunate not to beat Milan here.
"I think the Champions League inspires players and gets the best out of them, and I hope that is the case for our players.
"If we are to progress we have to pick something up away but we don't need to win.
"If we can get a point and beat Milan at home that gives us seven points and gives us a real chance of qualifying."
Lennon admits goalkeeper Fraser Forster will again be crucial to his side's chances and tipped the Geordie to win his first England cap in one of the upcoming friendlies against Chile and Germany.
"Regardless of how Fraser plays I think he has a good opportunity of playing (for England) anyway," Lennon added. "He has been in fantastic form for the past two seasons.
"Roy Hodgson has already indicated that he might feature in some of the upcoming games.
"Whether he does or not, that's up to him but if he did get the chance he is ready for it.
"He has shown great consistency at this level and he will again be important because we are away from home.
"Whoever the opposition is, they will create chances and if we want to get something out of the game then we need Fraser to play well."
You can watch Celtic take on Ajax in Amsterdam live on Sky Sports 4 from 7.00pm on Wednesday evening.