News emerged late yesterday claiming the Scotland international could miss up to eight weeks with the injury after damaging his hand in the wake of the Champions League third qualifying round defeat to CFR Cluj.
Lennon will consider going into the transfer market for a new goalkeeper after Scott Bain dislocated a thumb but is hopeful Bain will be back in action quickly.
"He dislocated his thumb," Bain said. "He's had a scan and we don't think he needs surgery. He is going to get a splint fitted and he should hopefully be back in training next week.
"We will assess it and get a fair idea of the extent of the damage and we will make a decision from there."
With Craig Gordon set to step in for Saturday's Betfred Cup clash with Dunfermline, Lennon insisted he was not already looking at strengthening in the position before Bain's injury.
"No, I had two good goalkeepers in the building," he said. "Craig is ready to play and he will start tomorrow."
Lennon is still looking for defensive reinforcements following Tuesday's defeat.
"We are working diligently in the background to bring players in and increase the quality and competition and strength in depth of the squad," he said. "The board have been absolutely top class with me.
"People are looking for divisions and destabilising. It's not there. We have to accept we lost the game, whether we deserved to lose it or not, we have to accept it and come back better."
The Celtic boss does not think the qualifying loss and knock-on financial effects will impact on his final dealings of the transfer window.
"I don't think so," he said. "We will still look to find players of value, quality and maybe re-saleable value as well."