Instead, Lennon is only more determined to increase the gap between his side and those that are in the shadow of a team unrivalled and unchallenged once again this term in the SPFL Premiership.
With their third consecutive title wrapped up several weeks ago, and on the cards before a ball was kicked at the start of the season, it would have been easy for Lennon's players to have cruised over the line.
That is not the mark of champions, however, and as his side sprint towards a finish that could yet see them accumulate more than 100 top-flight points, the Parkhead boss is only thinking about how to make his squad and his team even better.
Aberdeen have ruffled Celtic's feathers on more than one occasion this season as Derek McInnes' side ended the Hoops' hopes of a remarkable unbeaten Premiership campaign with victory at Pittodrie, weeks after dumping them from the Scottish Cup on home soil.
The Dons' renaissance in recent months has been much vaunted in selected quarters but they are still some way from getting anywhere near the best team in the country.
Celtic had only their pride to play for on Saturday when Aberdeen made their final trip of the campaign to Parkhead, but that was all the inspiration Lennon's players required as they clinched an impressive, deserved 5-2 win that, in the manager's words, "could have been a lot more".
It was another performance which showed that, while their exploits in the Champions League and two domestic cup competitions this season can be questioned and criticised, Celtic have little to prove in terms of their league form.
Victory at Parkhead, earned through doubles in either half from Scott Brown and Kris Commons and an Anthony Stokes strike that took him to 20 for the campaign, extended the champions' lead at the top to a massive 30 points.
It is a chasm that could well widen before the final whistle blows on the campaign on Sunday afternoon and one that shows no signs of diminishing in the longer term - not if Lennon has his way, anyway.
"We just want to finish the season strongly and we are doing that," he said in the aftermath of Celtic's 30th win of the season.
"We want to put a marker down to the other teams really to show that we have got a really good team here.
"We want to get stronger and we have done as the second half of the season has progressed with the players that have come in. We are looking like a good side."
The outcome may not have been surprising on Saturday, nor the fact that Commons and Stokes were on the scoresheet, but there was a welcome change to the norm for Celtic in the shape of the man who notched the remainder of the goal tally.
While his two main attacking talents have hit 50 goals between them this season, skipper Brown, doubled his Hoops tally for the campaign with a first-half brace.
Brown's efforts, both neat finishes after good work from Adam Matthews down the right flank, were a welcome sight for Lennon and the boss is eager to see his on-field leader chip in on a more regular basis.
"He has got that in his game and we are always encouraging him to shoot more," Lennon said. "I thought he had a fantastic game."
The sight of Brown twice wheeling away to celebrate may be an unfamiliar one this season but normal service was resumed after the interval as Commons ensured he wouldn't be outdone by his captain, his strikes ensuring efforts from Niall McGinn and Shaleum Logan were mere consolations for the visitors.
As has happened so often this season, the PFA Scotland Player of the Year was a central figure in many Celtic attacks, but it is his scoring ability - he now has 30 for the season - that has set him apart.
"There is creativity in the way he plays, his movement off the ball is fantastic and you always fancy him to score when he gets into those situations," Lennon said. "It has been a helluva season for him, he has been tremendous.
"We do use the formation to try and accommodate Kris as best we can. He is better centrally we feel than on the wing.
"He is far more productive in the central position because he can open teams up with a pass or change a game with the finishing power he has got.
"That is something that has pleased us, the way the formation has worked to accommodate him. He has really delivered for us in that position."
It was Commons who put the champions' seal on the victory with the final goal as Celtic settled a score, proved a point and collected another three.
The outlook for Lennon and his side is bright, but the signs are ominous for the rest of the Premiership.