Aberdeen have underachieved for decades but have had a change of manager with Derek McInnes succeeding Craig Brown, and have a strong squad following the acquisition of several new personnel during the summer.
Aberdeen put in a dominant performance against Kilmarnock in the first game of the new season, and the fans turned up to back the team to the tune of a 13,000-plus attendance.
And Celtic boss Lennon expects these elements to add up to the Dons providing a stern challenge in the inaugural Scottish Premiership.
Lennon said: "I would like to think that Aberdeen, with the size of the club and the resources they have, will be there or there about. But we said that this time last year.
"Motherwell have lost some influential players but they have recruited well again. Ross County have a nice bit of continuity about them and Inverness might surprise people again. But I’m thinking Aberdeen will push us more than anyone else. I think it is maybe their time now.
"The league needs another big club challenging," Lennon added. "If you look at the situation at Hearts, who are obviously a big club and suffering at the moment, it would be good to have a strong and vibrant Aberdeen in the league."