But the Hoops boss will continue to rely heavily on established pairing Gary Hooper and Anthony Stokes, who supplied the goals which gave the SPL champions a 2-1 win over Vfr Aalen here last night.
The ease with which the Bundesliga Two side took the lead has emphasised to Lennon the need for another central defender, and he admits: "This is a another priority because we only have three recognised centre-halfs."
With Emilio Izaguirre suffering from a viral infection, and Adam Matthews yet to kick a ball on this tour due to a calf injury, Lennon's backline is already stretched.
But Victor Wanyama has returned from international duty in peak form, and, along with Fraser Forster, is giving Lennon genuine hope that he will have a team ready to meet the challenge which Ajax will bring on Saturday when Celtic wrap up this tour.
The top scorer for the past two seasons, Hooper, got them off the mark in the 63rd minute of the game against Aalen when he slotted home a cross by Dylan McGeouch.
That brought Lennon's side level against the Bundesliga Two club, who had led from the fourth minute.
Not to be outshone, Stokes contributed what proved to be the winner 14 minutes from time after a rare piece of creative build-up involving Scott Brown and James Forrest.
With only two weeks until they compete in their opening Champions League qualifier, the draw for which will be made on Friday, there remains clear evidence that some degree of rustiness remains to be removed as the champions continue to integrate all of their first-choice players back into the side.
Nevertheless, Lennon is content that progress in terms of fitness and sharpness is being seen, and is satisfied that his side will be ready for this weekend's tough test.
The manager vocalised his frustration at how hard his side made it to overcome Aalen.
Sponsored by an energy technology company, and housing rows of solar panels along the roof of the two stands at their Scholz Arena, they proved too bright for below-power Celtic in the first half.
Judging by his cajoling, that was a disappointment to Lennon. Of the three teams he has selected to start in this tour, the one which was captained by Kris Commons against Aalen was by far the most recognisable.
The players who were given dispensation to return late from summer international duty are only now getting up to speed, and Wanyama and Mikael Lustig were far enough progressed to feature from the start.
They linked up with Kelvin Wilson and Charlie Mulgrew in a conventional back four, but, despite their physical presence and extensive experience, they got off to the worst possible start.
By the time Benjamin Hubner had opened the scoring, Forster had already made an important save from Marcel Reichwein.
The goalkeeper appeared to have once again thwarted Aalen when he blocked Hubner's initial close-range shot, the opportunity arriving for the defender following a head-flick from Robert Lechleiter, who had stolen in front of his marker at a free-kick.
However, the ball dropped back to Hubner off Forster's frame and he put it into the net from five yards.
Celtic had struggled to show any real urgency to regain parity by the interval. Indeed, Forster was still much the busier of the two keepers, his best save coming on 31 minutes when he touched another well-struck shot by the elusive Reichwein on to his crossbar.
The paucity of Celtic's attacking threat in the opening half could be measured by the fact Stokes had had their best chance, but, even then, home goalkeeper, Daniel Bernhardt, was not required to show his quality as the shot was blocked en route to its intended target.
Recognising the need to inject some urgency into his side's play, Lennon replaced Beram Kayal with Brown for the second half, and quickly added McGeouch, Paddy McCourt and Mo Bangura to the action.
The response was almost immediate, with McGeouch's accurate cross setting up Hooper for his well-taken goal, then Brown playing his part in Stokes's winner before the club captain found time to pick up his second booking of this tour.
More importantly, Celtic got their first win and now travel to Holland in better condition and mood.
VFR AALEN: Bernhardt: Traut, Kister, Hubner, Buballa; Dausch, Hofmann, Grech, Kampl; Lechleiter, Reichwein. Subs: Wehr, Barth, Haller, Valentini, Bergheim, Junglas, Klauss, Ruiz, Weiss, Zimmermann, da Silva.
CELTIC: Forster; Lustig (McGeouch 61), Wilson, Wanyama (McCourt 62), Mulgrew; Kayal (Brown 45), Ledley; Forrest, Commons (Bangura 64); Hooper (Murphy 73), Stokes. Sub not used: Zaluska.
REFEREE: Dr Felix Brych.