Had they lost to the Dutch masters, it would have been Europa League or bust as the door to the last 16 would have slammed shut with only half the campaign gone.
That would have been disappointing, given what they achieved last season, but it would have been no disgrace.
They are, after all, the team from the bottom pot in the 'group of champions'. So, finishing anywhere other than fourth means they have punched above their weight.
But Lennon believes that, while his team are still standing, they can deliver a knockout blow to bigger opponents.
James Forrest did precisely that when he rammed home a penalty two minutes before half-time after Anthony Stokes had been bowled over by Stefano Denswil.
Beram Kayal made it a quick one-two with a deflected shot nine minutes after the break, a blow to the solar plexus from which Ajax could not recover.
Not even the straight red shown to sub Nir Biton two minutes from time for a high tackle on Thulani Serero could swing the decision away from the Hoops who, for the second European game in a row, finished with 10 men.
By the time sub Lasse Schone managed to get the ball past Fraser Forster in the 93rd minute, the bell for the end of the contest was already about to sound.
Relieved though he is to finally get going, both in terms of goals and points, before he travels with his side to Amsterdam in a fortnight, where third place - at least - can be all-but secured, what must still frustrate Lennon is that this has been made much more of a catchweight contest because Celtic have been forced to fight with one arm behind their back.
The loss of Victor Wanyama, Gary Hooper and Kelvin Wilson in the summer was a blow.
With Scott Brown, Kris Commons and Adam Matthews also counted out of last night's tie, it was always going to be tough for Celtic to lay a glove on Ajax, let alone put them down.
But they came out swinging and refused to yield, finally getting the victory their efforts in this season's Champions League has deserved.
Lennon said it was a game they didn't have to win, but, if they lost, he conceded it would mean curtains to contesting for a place in the last 16.
That stark warning was heeded by his players who, to a man, stood firm against the Dutch.
The manager's extra scouting mission to Enschede at the weekend reminded him just how adept Ajax were at pinging the ball around, seemingly glued to the surface.
However, passing across Celtic's back line rather than through it meant they struggled to fully test Forster for the majority of the game.
Viktor Fischer and Kolbeinn Sigthorsson were expected to pose the Hoops defence - marshalled well by Virgil van Dijk - much more trouble, but flitted in and out to little effect.
Indeed, it was from a set- piece midway through the first half that Ajax finally gave Forster a fright, Christian Poulsen's shot after the ball had flicked off van Dijk's head smacking off a post and back out.
Little wonder Frank de Boer looked the more exasperated of the managers.
Pretty patterns his side may have woven, but Celtic were the ones who got the points sewn up.
With Stokes playing up ahead of Teemu Pukki - who sliced a great chance well wide in the first half - there was no real physical presence to the Hoops' attack.
But there was enough support from Forrest and captain Georgios Samaras to keep the Dutch engaged.
With Kayal - preferred to Joe Ledley - and Charlie Mulgrew providing a midfield platform, the absence of so many important players was effectively camouflaged, if not quite negated.
Kayal - so often an observer not a participant when the big games come to town - reminded everyone what he could bring to the party before the break when he raced back to halt Fischer's breakaway from a Celtic corner which had come to nothing.
When he later popped up on the edge of the opposition box to send a shot through a ruck of players and in at Jasper Cillessen's right-hand post, it was more than anyone could have expected from the Israeli.
Forrest had also made a telling contribution, keeping calm for the couple of minutes between Stokes being bundled over on the left edge of the box until the spot-kick was finally taken, during which Van Dijk was booked along with Poulsen.
That was the first Euro goal Celtic had scored since the same kid rammed home the shot which saw Celtic safely past Shakhter Karagandy in the second leg of their play-off.
Like that night, Forster was there when called upon. And his save when Serero got through one-on-one with him at the start of the second half was vital, given the second goal for Celtic did not arrive until two minutes later.
The man with Rio in his sights was also called upon to make a couple of decent diving saves as Ajax chased the game late on, but was up - or down - to the challenge, until Lasse Schone denied him his clean sheet in stoppage time.
But it was not a night when two or three men had to step up to the plate: the entire Celtic side had to do their bit, and they did.
It's a spirit and camaraderie which has already taken this group of players far, and Lennon is sure the journey is a long way from over.
The next stop is Amsterdam and another massive occasion and huge test of their resolve.
But with the points advantage now established over Ajax, the pressure is all on the Dutch.
They are the team facing a European exit post-Christmas, though they will feel they did enough to take something away from Celtic Park.
Like so many before them, however, this amounts only to memories of a special atmosphere in a real football theatre.