Brown has been playing through the pain barrier for most of the season and it had been expected that he would go under the knife at the end of the group stage.
That would have allowed him time to recover before the knockout phase begins in mid-February, but Lennon said the club captain is feeling positive.
"He's feeling good and remarkably again had a great game for us the other night," Lennon said. "He doesn't want to have the surgery so we are going to manage him the best we can.
"We can't force him to have surgery, although eventually our medical team thinks he will require it. It's not like we are soft-soaping him through training now, he is training all the time.
"He has obviously had a positive reaction from the last injection and we will just keep going. We need to chat about it. If and when the surgery is required we will need to plan the period he is going to be out, because we would like him for the last-16.
"I don't think he would (miss the last-16) if he had it now. It's an eight-week period of rehab.
"I haven't really had a chance to speak to him or my medical team but he wants to keep on playing. But we don't want to put him through what we put him through the last two months."