At this moment, they are at the halfway point of this schedule of matches.
Tomorrow, the Hoops boss is looking for a significant improvement when his side – augmented by some of the internationalists who have all reported back after extended summer breaks – play VfR Aalen, a Bundesliga Two side.
Stuttgart Kickers – just like Augsburg before them – managed to spike all of Celtic's guns, and the Third Division side went one better than the Bundesliga team by scoring one themselves.
Defeats, in themselves, mean nothing in pre-season. But the accumulation of not creating many chances and taking none of the ones you do, can be a reason to worry, especially with Champions League qualifiers looming large.
Gary Hooper, Anthony Stokes and Daryl Murphy have all been tried in these two games and it is clear they are some degree short of being on fire.
Of course, it might only take one good night, hopefully tomorrow night, to spark them into life.
But the thought of heading to Amsterdam on Saturday to take on Eredivisie champions Ajax with little happening in the final third is not a prospect which will appeal to Lennon.
The emphasis now will move from conditioning to sharpness in pursuit of finding that edge, then attempting to hone it – and quickly.
There is little doubting the goals are there – Hooper hit five in his last competitive appearance – but they need prised out, and the sooner the better. With each passing pre-season game, the fitness levels are rising. It's just the strike-rate that remains cemented to the floor.
"The only disappointing thing for me was our play in the final third in the second half of the game," said Lennon as he reflected on last night's defeat.
"We probably didn't work the keeper enough. But the condition of the players is coming on well.
"We are injury-free, which is a big bonus."
The one exception to that is Adam Matthews, who continues to struggle to shake off a calf injury which has prevented him playing any part in either of the games to date.
With a handful of the younger players who have been here to give the squad some depth now heading back to Glasgow to take part in Saturday's game against Partick Thistle, the likes of Georgios Samaras, Emilio Izaguirre, Victor Wanyama and Mikael Lustig will come into the frame.
They will require some time to get up to full speed, but will bolster the team.
Slack defensive play allowed Omar Jatta to head past Lukas Zaluska four minutes before half-time last night. With Marcos Alvarez, Kevin Dicklhuber and Sandrino Braun spurning good opportunities against a tiring Celtic side in the closing minutes, the defeat could have been much heavier.
Lennon was able to make seven changes from the line-up that started against Augsburg.
Captain Scott Brown was among those to see his first action of the tour, while Thomas Rogne and Kris Commons had recovered from the slight strains which left them on the sidelines against Augsburg.
The Celtic players wore black armbands and a minute's silence was observed as a mark of respect to Joe McBride, who passed away last Wednesday.
It would have been fitting had Celtic then proceeded to deliver the type of attacking display for which the former striker was renowned.
However, with Murphy and Hooper paired up front, while there was power, there was very little pace.
This was reflected in the fact that, in the first half, Celtic's best two chances to open the scoring had come from a Rogne header after he rose to knock down a Commons corner, saved at full length by agile keeper Daniel Wagner, and a shot from Commons himself as he slipped on the lush turf which dropped over the crossbar.
Murphy and Hooper had provided willing targets for a midfield which saw Commons at the head of a diamond, and Paddy McCourt sitting deep to pick up the ball from his defenders.
Lennon expected that, having removed some of the rust and rough edges in their first game, this would be a much more coherent and assured performance. There were signs of improved fitness, but not enough to allow Celtic to take control of the match.
Prior to conceding, Celtic had restricted Kickers to a few long-range free-kicks, none of which really troubled Zaluska, who was not required to make his first save until 29 minutes had elapsed, when he coped easily with Mahir Savranlioglu's low drive.
Patrick Auracher's header from a free-kick should have been a warning to Celtic that they were not marking tightly enough, but they were caught sleeping four minutes from the break when Fabio Leutenecker got to the goal-line and found the head of Jatta with his driven cross.
Lennon's decision to introduce James Forrest, Kelvin Wilson and Beram Kayal for Charlie Mulgrew, Andre Blackman and Hooper indicated the manager was determined to avoid a bloody nose, even in a friendly.
The sight of Forrest on the ground, holding his left ankle, after an accidental collision off the ball with Savranlioglu, was of more concern to the Celtic boss who was relieved to the see the 21-year-old, who missed the final three months of last season with an injury to his other ankle, return to the action after treatment.
Brown was also in the wars, and Jerome Gondorf was left in no doubt what the captain thought of his latest tackle.
Commons summed up the night when his free-kick flew out of the stadium and into the trees, causing him to be replaced by Radiu Ibrahim.
By the end, the traffic was all one way, and Celtic's quest for that elusive first goal now moves onto Aalen.
STUTTGART KICKERS: Wagner; Evers, Leist, Auracher, Stadler; Leutenecker, Marchese, Jatta, Gondorf, Savranlioglu; Gruttner,. Subs: Krauss, Braun, Ivanusa, Sprung, Gerster, Dicklhuber, Fennell, Schmidt, Alvarez.
CELTIC: Zaluska; Toshney (McGeouch 64), Rogne, Mulgrew (Wilson 45), Blackman (Kayal 45); Brown, McCourt (Watt 71), Commons (Ibrahim 76), F Twardzik; Hooper (Forrest 45), Murphy. Sub not used: Forster.
REFEREE: Marco Fritz.