What that man will walk into is much clearer.
The squad Henrik Larsson, Owen Coyle, Roy Keane, Davie Moyes, Malky Mackay, Jackie McNamara, Oscar Garcia, or whoever gets the gig, will inherit, has more top-line strength than genuine depth.
However, it is in much better shape than the group Lennon was handed when the last leadership change took place, in March 2010.
The dispirit and dispirited bunch cobbled together by Tony Mowbray in the two transfer windows he was in charge had heavily underachieved and needed to be disbanded urgently.
That took time - and money - as players Lennon quickly identified as surplus to requirements and a drain on the club's resources were not in a hurry to leave a team they had just joined, most on decent wages.
The cost of persuading them to move on was set against the funds available to recruit the men Lennon wanted to start afresh.
And, after a very busy summer of comings and goings, the rookie boss found out the real cost of operating in such a state of flux as his new-look side bombed in both the qualifiers for the Champions League then Europa League.
There were real shades of Gordon Strachan's first faltering steps as Hoops boss.
He succeeded Martin O'Neill in the summer of 2005, and quickly established that, through a process of slashing the wage bill and contracts of an ageing squad coming to an end, he had only a dozen players with genuine first-team experience available to him.
One of them was Bobo Balde, who was actively negotiating his own exit from Parkhead.
Craig Bellamy was willing to make his loan from Newcastle permanent, but that would have devoured all of the budget Strachan had to rebuild.
As welcomed as that signing would have been among the fans, Strachan decided the money had to be spread much more widely, to fill six or seven positions.
Against that backdrop, and with players trying to settle into a side still suffering the hangover of losing the league title on the final day and the departure of the manager who had become so synonymous with the rebirth of the club, the qualifier against Artmedia Bratislava arrived.
Strachan, like Lennon, bounced back remarkably well from this early serious setback in Europe to go on to lead the club to three SPL titles in a row and into the last 16 of the Champions League.
The next man to take up mantle of Celtic boss will be in a much better position, in terms of the side he finds awaiting him.
Lennon used 31 players over the course of last season as he attempted to compete on the domestic and European fronts.
It proved a challenge too far. Though the performance throughout the league campaign was the most impressive of his four years as boss, the way they capitulated in the second half of the Champions League campaign was alarming and spoke of the lack of quality in depth in the squad.
The damage done with the sales of Victor Wanyama, Gary Hooper and Kelvin Wilson - since then Joe Ledley has also departed - was never more evident than in the last three group stage games against Ajax, AC Milan and Barcelona.
Some improvement was made to the squad when Stefan Johansen and Leigh Griffiths were bought in January, but they remain untested in a Celtic strip in Europe.
The improvement shown by Nir Biton before he picked up an injury which prematurely ended his season is another positive, as is the emergence of 18-year-old Liam Henderson as a genuine contender for a first-team place.
But Lennon left the club acknowledging there are four or five positions which need to be addressed, and the man who succeeds him is unlikely to consider it is any less.
Indeed, it could be even more if Fraser Forster, Virgil van Dijk, James Forrest or any of the other key cogs in the Green Machine are sold when the transfer window opens next week.
If any or all of the aforementioned - the club's best players in Europe - depart, it will reduce significantly Celtic's quality rating and ability to be competitive on the big stage.
The chances are that, as per previous incumbents of the hot seat, the new boss will be told the price of the players he can afford to bring in will not match the fees received for the men going out.
It is seriously unlikely any overspend will be permitted. Mowbray was the last manager to exercise that right, spending more than he generated, and Lennon paid the price for that. It took him a couple of years to recover from that profligacy, and it is to his immense credit that, over the course of his time in charge, the club made a profit of almost £14million in terms of players sold to those brought in.
The $64m question is, how rich or impoverished has this left the current squad, and does the surgery the next manager must perform on it require to be radical or cosmetic.
These are discussions sure to take place at the interviews Dermot Desmond and Peter Lawwell will be conducting with the potential candidates.
But, in six days, the transfer window opens for business, and four weeks from now, pre-season begins. So the clock is ticking.