The Hoops midfielder is waiting on results from a specialist and if an operation is necessary, it would likely mean him missing the second leg of the Champions League tie at Juventus on March 6 and Scotland's World Cup qualifying double-header against Wales and Serbia later next month.
Ahead of the visit of Dundee in the Clydesdale Bank Premier League on Sunday, Lennon said: "The specialist is coming back with his prognosis. He may need surgery but we won't know that until Monday, the specialist is on holiday at the minute.
"We are expecting the specialist to say he may need surgery so as soon as we get him a slot, if that is the case, then we will get it done.
"He is a very important player, the captain, but the squad is strong."
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