When he wants desperately to be working through the problems afflicting his team, many of them are scattered to footballing outposts across the globe.
Others are holed up in the treatment room at the club's training complex, divorced from the action by a plethora of breaks, strains and tears.
Worse still, the international break serves as a serious barrier to any opportunity Lennon may have to show his players where they are going wrong – and, more pressingly, pointing them in the direction of putting it all right.
Already, the next fixture, at Kilmarnock a week on Saturday, is occupying his mind.
Who will be available? How they should line up? Which Celtic will show up on the day? All questions which are, as yet, without an answer.
What is known is that they will go into their 10th SPL game of the season 10 points behind Rangers.
Also confirmed is that Kris Commons will be an absentee after his self-inflicted suspension, the legacy of a moment of madness at Tynecastle on a day when all that ails Celtic came to a head.
The third league defeat of the campaign has to be a watershed. There has to be a response, of the positive, consistent and immediate variety.
However, the international hiatus prevents at least the final element of this from being enacted.
Hence the reason Lennon and his management staff can only sit and brood, counting down the days until his players return to the fold.
To his credit, he is trying to find some positive from this impediment, and finds it in the clearing injury list.
It is too easy to shelter behind the fact you have been denied the use of players. After all, every manager has to contend with such problems.
However, when you consider Lennon went to Tynecastle without Emilio Izaguirre, Kelvin Wilson, Scott Brown, Beram Kayal, Joe Ledley, Glenn Loovens and Cha Du-Ri – all of who would have strong claims to be first picks – it is to the manager's credit that he does not try to offer this as an excuse.
"The break for the internationals will be good from the point of view of the injuries we have," said the beleaguered boss, who watched the men he does have fit and available drop another three points less than 72 hours after the exertions of a tough Europa League tie.
"Between the Thursday and the Sunday, you don't have a lot of time to work with the players on shape or things like that. But I don't think that was the problem at Tynecastle.
"So we may have to look at changing personnel or we may have to look at changing the formation because, obviously, there is something not quite right."
Of that there is no doubt. What Lennon can do to alter this is what is being debated across the Celtic diaspora, and beyond.
He is already talking about movement. But the fact is, within the restrictive confines of the transfer window system, until January he has to work with what he has got.
"Hopefully, Ledley and Kayal will be fit for when we start playing again," he said, searching for some light at the end of this dark tunnel.
"Beram has a thigh injury which he picked up after the Udinese game last week."
The influential stand-in captain was a big miss at Tynecastle, and his participation for his country in their Euro qualifier against Malta next week is now in doubt.
Kayal, like Brown and Cha, has previously returned from international duty damaged, and Lennon can only hope there is not more of the same this time around.
Will he be relieved when the club calendar stops being interrupted by these commitments? "Yes, because we have lost important players after they have been playing for their countries, and we can't afford to lose any more," he said.
It is a huge bugbear for club managers, and a particular irritant for a boss who already oversees a stretched squad. Lennon accepts it goes with the territory, and seeks no sympathy. "We have injuries, but I feel the squad is decent," he said.
The absence of so many has opened the door for others, and Victor Wanyama is proving to be a shining beacon in these gloomy days.
The 20-year-old Kenyan impressed against Udinese, and built on this among the despair of Sunday. "I thought Wanyama again had a decent game," agreed Lennon.
The midfielder is one of the few who merited pass marks, though Fraser Forster reacted in the correct way to being dropped for the Europa League tie with a more confident performance.
"He made a great save in the first half, and we can't really blame him for the goals," said Lennon. If only that had been the case in other areas of the pitch.
Early opportunities missed set the tone, and one theory is that the fact they went into the match trailing Rangers by 10 points got to the players. But Lennon disagrees. He explained: "We never really mentioned that. We just said, 'Look, this is a game you have to win'.
"I was pretty pleased with the first half, without being overly enthusiastic because we should have been at least a goal up.
"Mo Bangura had missed a simple chance with a header, and Kris Commons had a couple of chances as well. We just asked for a little bit more in the final third. But we didn't get that."