The manager travelled to Turin immediately after the defeat of Hearts to watch AC Milan draw with Torino and his flight may well have been spent reflecting on the testimony of Tynecastle before coming to a judgment on his selection for San Siro.
The form of Anthony Stokes has given the manager a sharp nudge as he takes his pen out to complete the team lines. The order for the San Siro would normally be for Celtic to pack the midfield, and place all hope on Georgios Samaras as a forward who could relieve the defence by running hard and long, and flicking headers on to supporting midfielders.
Lennon, though, has more options, even if containment must be a priority. First, he will hope that Virgil van Dijk can be the centre-back who has performed in the SPFL Premiership rather than the one who played in Kazakhstan. Second, he knows his team now has pace.
Samaras, a frustrating presence in front of goal as was evidenced by his missed chances against Hearts, is a dedicated and forceful runner on the counter attack. James Forrest and Derk Boerritger, who produced two marvellous crosses against Hearts, are quick and technically adept. Adam Matthews can also supply speed in wide areas and Teemu Pukki, the £3m signing from Schalke, showed on Saturday he is certainly brisk, particularly on the turn.
However, it is Stokes who holds the key to Lennon's selection on Wednesday. It is difficult, if not impossible, to imagine the Celtic manager omitting Samaras, who has found scoring goals in Europe as easy as he finds it difficult in the Premiership. The experience and strength of the Greek is something Lennon admires on foreign fields. But Stokes has made himself a contender for the San Siro, even if he may be restricted to the bench. The Irishman looks fit, revitalised and committed to making an impression for Celtic this season after a campaign dogged by controversy and injury.
He was instrumental, with his incisive run and cross, in providing the late winner that knocked out Shakhtar Karagandy to allow Celtic to progress to the group stages of the Champions League. He scored the winner against Dundee United and scored one and played a significant part in the two other goals against Hearts. Most impressively, he was intelligent and willing in his movement, with his aptitude for running offside restricted to a moment in the first half when he was just too keen to apply a finish to a cross ball.
The questions over Stokes have never concerned his ability to score goals but he has been overlooked for major games, particularly in Europe, for valid reasons. Can he hold the ball up? Can he link with other players in pressurised situations? Can he do the running that saps the spirit as well as the legs? He answered all three in the affirmative against Hearts.
The calibre of the opposition, however, means that the Irishman's suitability for the Champions League can only by answered when he plays in the competition. This comment is not to denigrate Hearts. They were committed, hard-working and organised against Celtic with Kevin McHattie impressive. But they are also young and inexperienced.
Gary Locke, their manager, had no questions about his side and was rightly impressed by their attitude and belligerent defiance. He had cause, though, to ponder the award of a penalty when the ball struck the arm of Jamie Hamill. Willie Collum, the referee, either awarded the penalty for Hamill's grappling with Stokes or believed the midfielder had his arm in an unnatural position, or even moved his arm to ball. The evidence for any of the above was hardly convincing.
As Locke gains consolation that the performance of his side can render the 15-point penalty as an obstacle to be overcome rather than a sentence of relegation, Lennon can be pleased that his side showed speed, occasional flair and the sheer doggedness to win when their minds might just have been distracted by the Champions League.
The Celtic manager had thus completed successfully the first item on his post-international agenda by leaving Tynecastle with three points and a highly satisfactory performance gilded by a debut goal from Pukki.
He will approach the San Siro with some apprehension but emboldened by the campaign last season. His players, too, have an added confidence though Stokes merrily admitted that his absence from Champions League matches left him exempt from any of the added gloss provided by the successful emergence from a group containing Barcelona, Benfica and Spartak Moscow.
He may just provide an answer to Lennon's continual reflections on selection in a build-up to the first match of this year's group stage. Once he has resolved the team lines, Lennon and his players will then face an unrelenting barrage of questions from AC Milan.
The examination will be demanding but it the opportunity of growth through experience, and not just for Stokes.