McGrain, who is now part of the first-team coaching staff, has watched with interest as Lennon has gone about building up a side from the one he inherited three years ago from Tony Mowbray.
The Hoops boss marked his 200th game in charge of the club with the 7-0 mauling of Hearts at Tynecastle on Sunday and McGrain reckons Lennon has matured into the Celtic job.
"He has grown mentally and he is still learning," he said. "I am sure that he will have learned a great deal from the European ties.
"He is finding out what team to pick and who to play where. He knows his players better than anybody and Garry [Parker] and Johan [Mjallby] work hand-in-hand with him."
Meanwhile, Celtic have been paired with Aberdeen in the fifth round of the Scottish Cup and McGrain believes that the Hoops will be inspired to defend their trophy because the sight of another team celebrating in the final at Parkhead would be a difficult one to take.
"It is the last game of the season," he said. "If you didn't win - and I lost a couple - it was always a long summer.
"If you lose the game and you see the other players running around the park it is hard to take. Certainly you wouldn't want to see another team running around celebrating at Celtic Park."