No sooner does he approach what he reckons will be completion of the job, than he knows he must start it all over again.
Building a Celtic team has no end point. There is no estimated time of arrival when you will reach your goal and can kick back to admire your work.
It is a never-ending evolution, the conditions dictated as much by circumstances outwith your control than by that over which you hold sway.
Which is why it is essential, at the end of every campaign, to step off the wheel, at least briefly, to indulge in a period of serious reflection.
Before you replenish, you must take stock of what you already have and where you currently stand.
Having exited a season of ups and downs - the high points being the most-emphatic retention of the league title and qualification for the Champions League, the deepest dip the form in the cups and in the second half of their group stage schedule - Lennon has much to mull over.
And, for the first time, he is doing so without any input from the man who has stood by his side for the past four years, assistant boss, Johan Mjallby.
Coach and close confidant, Garry Parker, will, of course, have his say.
But Lennon already has a clear vision of how the squad rates compared to the one which preceeded it.
At this date last year, it could still boast talent of the quality of Victor Wanyama, Gary Hooper, Kelvin Wilson and Joe Ledley, all tried and trusted on the European and domestic stage.
So, after all last summer's comings and goings, did Lennon consider he entered 2013-14 with a better squad than before, as numerous people -including skipper Scott Brown - had claimed at the time?
"No," replied the manager before adding the all- important caveat, "But it is improving.
"It took me three years to get to where I wanted to be with the squad I had last season. Now we are building again.
"I'm pretty happy with the way it has taken shape in the second half of the season.
"I think we will see more next season from Nir Biton and Stephan Johansen, even Liam Henderson coming through.
"That will augment the core of players we already have, with the likes of Virgil van Dijk having had a brilliant first season.
"That's given me a lot of confidence going into next season."
Utopia in Paradise would be to gather a group of improving players, and to hold on to them all until they reach their full potential.
However, that is not the Celtic business plan.
Discovering, developing then selling at a profit is.
Frustrating though that clearly is for the man in the hot seat charged with maintaining standards throughout the state of flux, Lennon knows there is nothing he can do but live with it.
He acknowledged: "You always want to build long-term, but you can't. So, you have just got to do it season by season."
The plans are already being laid for his team No.4, or is it No.5?
With the departure of Georgios Samaras, only Lukasz Zaluska and Brown - James Forrest was still in the Development Squad - survive from the disjointed first-team squad he inherited from Tony Mowbray in March 2010.
The turnover reflects how much work initially he had to do when he was installed in his first managerial post, and how it continues to be done to keep the club at the level they need to be.
The faces may change, but the challenge at the start of every season remains the same: To retain the title, qualify for the Champions League, and try to add any other silverware they can.
In the process, Lennon is entitled to enjoy the personal achievements of some of his players, and take pleasure from aspects of what the team collectively has produced.
"The consistency we showed in the league, that, and qualifying for the Champions League in a really difficult period of the season," is his answer when asked what gave him most satisfaction in 2013-14.
"Also the emergence of Virgil van Dijk, and Fraser Forster making his England debut at Wembley."
Forster, Van Dijk and Co. came within one match of an unbeaten league season as they amassed 99 points. But Lennon has no regrets.
"Losing that game to Aberdeen [having gone 26 unbeaten in the title race until that February night at Pittodrie] does not put a blot on what has been a fantastic campaign," Lennon mused. "How can it?
"The cup match we lost to Aberdeen annoyed me. But, I can count on two fingers the number of games I've been upset with the players this year.
"I think the players have been fantastic. They get taken for granted, and there is an expectation they should go out and steamroller teams all the time.
"That is being disrespectful to the opposition. Over the piece, we played some brilliant football, and I don't think too many people can complain about the performances.
"All we can do is keep winning the games and keep improving, and we are certainly doing that. We improved our league points total this year [from 79 in 2012-13 to 99]."
Soon, it will be time to try and do it all over again, with the players due to report back for pre-season training in 32 days.