The Hoops beat St Johnstone 2-1 on Scottish Premiership duty on Saturday but with important Champions League fixtures ahead, the Hoops boss plans to rest some of his key figures.
Lennon has promised to use his squad, which could open the door for Israel midfielder Nir Biton to make his full debut.
Tom Rogic, Dylan McGeouch and Georgios Samaras - all of whom were on the bench for Saturday's 2-1 victory over St Johnstone - are others in contention.
Beram Kayal and Joe Ledley (both groin) miss out along with James Forrest (virus) and long-term absentee Steven Mouyokolo (Achilles).
Definitely not featuring against their Greenock opponents when they visit Celtic Park will be injured midfielders Beram Kayal and Joe Ledley (both groin), winger James Forrest (virus) and long-term victim Steven Mouyokolo (Achilles).
Lennon is desperate to land the only domestic trophy he has so far yet to win, although he does expect to alter his team after their weekend exertions against St Johnstone.
The Northern Irishman said: “The League Cup was the first competition that I won as a player here and first I won as a captain, so it does have some significance for me personally.
“We have only won the trophy 14 times. Even if you go back to Mr Stein’s time, it’s not been a competition that we have dominated. But it’s a competition that we are in and one that we want to win.
“There are a few players who will need a break and we will change the team from the weekend. But they won’t be drastic changes and we will treat Morton with the respect they deserve.”
Morton are again without Thomas O’Ware, who has a foot injury, and Joe McKee (ankle) as they make their first trip to Celtic Park in nearly 16 years.
Dougie Imrie is back in manager Allan Moore’s plans despite being substituted at half-time as the Greenock men went down 2-0 to Queen of the South at the weekend.
Moore said: “I had wanted us to be heading to face Celtic with a good run of form behind us but that is not the case.
