The Cappielow side may hope they will face a much-changed Hoops team at Parkhead, but Lennon is not taking any chances.
He reminds everyone that, with two championships and two Scottish Cups to his name, this is the one piece of domestic silverware to elude him since he became a manager.
And, at the fourth time of trying, he aims to put that right.
For a competition which requires only four victories to lift the trophy, it has provided a litany of bitter disappointments for Lennon the boss, who won it twice as a player.
His record reads: 2010-11 lost 2-1 to Rangers in the final after extra time; 2011-12 lost 1-0 to Kilmarnock in the final; 2012-13 lost 3-2 to St Mirren in the semi-final.
Little wonder the Hoops boss intends to send in his big guns against Morton. Lennon said: "This is the one domestic trophy I have not won during my tenure here as manager. And it's one I would like to win.
"Morton will come here and enjoy the night out and have a go. We have to make sure there is no upset and keep the momentum going because there is a bit building here."
Lennon continued: "I would like to make changes for this game, but you can't go overboard with it.
"I want to get through to the next round, so we have to find a balance.
"Some players need to play and some are still getting to grips with the British game.
"But, to say we have a massive squad to cope with everything, that is rubbish."
Lennon is reluctant to speak about it as this early stage, but he wants to become only the third Celtic manager - after Jock Stein and Martin O'Neill - to claim a treble.
However, he knows only too well that one off day or night can destroy the dream for another year.
"We are well aware that a slip-up in any of the rounds and you can be out of it," said Lennon.
"I am just concerned, more than anything, about injuries building up. Which is why there has to be a balance there.
"Joe Ledley picked up a groin injury last weekend, and he is going to be another week or two.
"We are hoping that Mikael Lustig will be all right for tomorrow, but we don't think Adam Matthews will make it for this game.
"He felt his hamstring getting tight on Saturday, and also got a kick on an ankle.
"James Forrest has a virus. He will be in today, but obviously he will not train, and I don't now when he will be able to rejoin us.
"So, I have just got to use my squad as best I can."