Brown missed Saturday's 4-0 win over Motherwell because of an ongoing ankle problem and Lennon hopes he can make it for the vital matches in a huge week for the Glasgow club.
"It is one of those injuries where he needs rest but with the fixtures it is difficult to give him that rest," said Lennon.
"He tweaked it a little bit on Thursday and it was too sore to even train on Friday.
"It's not like Scott to be like that, if he pulls out of training he must be in a bit of pain.
"So we will see how he is on Tuesday and hopefully he will be okay for Thursday.
"He is such a good player and a valuable player for us, I don't like leaving him out at any time and Thursday is a different type of game.
"Away from home in Europe he is the type of player that I would want in the team.
"We are hoping he will get through the two games but I will have to be advised by the medical team on that and obviously Scott himself.
"If I could choose it would probably be Sunday for the league is the priority. But it would be a bonus if we had him for both games."