Lennon was expected to go once Celtic lost to Ross County at home on Sunday and crashed out of the Scottish League Cup.
Protests erupted outside Celtic Park after the game and the players had to leave the stadium under police protection as the pressure on the board to act moved a notch higher.
But Celtic board took the surprising decision to stick with him earlier this week and it has led to criticism with many fans believing that sticking keeping Lennon will further damage their season.
Rough feels the decision on Lennon’s future at Celtic has only been postponed and he needs to get results in the next few games if he does not want to force the board’s hand.
He also believes that the Celtic board could be looking at his overall record and the fact that he has lost only two domestic games this season.
Rough said on PLZ Soccer: “We all know it is only a stay of execution, and the only way he gets out of this is by winning games.
“The Ross County one, I would have thought that would be it because getting beaten by Ross County at home is a bad one.
“I would hope the board would look at the bigger picture and look at what he has done for the club as a player and a manager, he has won five trophies since he came back in.
“I know a lot of the stats are being thrown at his door, but if you look at the biggest stat, he has played 22 games this year and he is lost six, four of them were against European sides.
“Maybe that’s what the board has looked at, maybe they believe that this month is something that can be turned.
“The only way do it is through the players in the park and winning games and Lenny will know.”
Despite all the pressure, Lennon will be in the dugout at the San Siro when Celtic take on AC Milan on Thursday night.
