Lennon also revealed that the midfielder, who has been struggling with an ankle injury, would be sidelined for Scotland's upcoming Euro 2012 qualifiers against Liechtenstein and Spain.
"Scott is going to see a specialist again in the next few days," said Lennon. "I don't think it will require surgery but it might just be that it will take a bit longer than we first thought.
"It might have been detrimental that he was playing without being fully recovered. So he will go and see a specialist over the next few days and we will know the prognosis after that."
Meanwhile, Udinese will be without influential striker Antonio Di Natale, who hasn't travelled to Parkhead.