Brown's injury meant he missed Saturday's 1-0 home win over Aberdeen which got the Hoops' defence of their Clydesdale Bank Premier League title off to a winning start.
Lennon said: "Scott had a scan on his hip and he has a bit of degeneration in there, on the disc. Whether we can get him through Wednesday... we will see how he is on Monday."
He added: "He was very sore yesterday and it's not like Scott. It might mean an injection and hopefully that will calm it down. It might need to be seen to down the line but it is not a massive concern for us at the minute. It is never a risk when you play Scott but we will work closely with him over the next couple of days and see how he is."
The champions struggled until the 79th minute when Dons keeper Jamie Langfield made an horrendous mess of Kris Commons' shot at his near post after the Hoops midfielder had played a short corner with Joe Ledley.
Lennon will have winger James Forrest back from a groin injury while stand-in skipper Georgios Samaras, who came off early in the second-half still suffering from a head knock he had taken early in the game, should be okay.
The Northern Irishman said: "Forrest will be fine. Samaras got a kick to the face today and he felt a big groggy, he wanted to give it 10 minutes after the break. He is still feeling dizzy so we will have to see how he is, but he should be okay. Charlie Mulgrew was suspended so he will come back into contention."
Aberdeen boss Craig Brown refused to blame Langfield directly and would not discuss the possibility of dropping him for next week.
"I am not going to make a decision on that just now but I am not going to condemn," he said. "If you left out every player for making a mistake you would have no team for next week.
"I will never criticise an individual. I am criticising the team for not responding appropriately to the short corner. They had clear instructions and switched off momentarily."
Source: PA
Source: PA