Now he wants to return the SPL trophy to the club after an absence of three years.
Lennon is confident the ground work done in his first season in charge has laid the foundations for another serious tilt at the title which eluded them by just one point.
However, with major upheaval across the city at the home of their rivals, Lennon is reluctant to make any massive predictions or promises – other than that he is more determined than ever to wrest the championship from Rangers.
As he prepared to lead his squad to Australia for their warm up games, Lennon said: "We were disappointed we never won the title because that was our priority, so we will double our efforts next season.
"But I think the board recognise the strides the team made this year.
"It's been wonderful, and I also can't thank the supporters enough. The atmosphere at Celtic Park was as good as I've seen it here for a long, long time.
"But what I want to do is bring more trophies back and, hopefully, the thunder will come back even more."
Along with that growing support comes growing expectation. But this is something Lennon regards as a torch to carry – not a burden.
He said: "I haven't yet sat down with the backroom staff to go over what happened last season, but we'll try to do that over the next few days.
"At the end of the season there wasn't a lot wrong with the way we played. Some of the football was fantastic and we want to continue that.
"We weren't far away from achieving a domestic treble, but we fell short in two competitions and we want to improve on that.
"That's the difference between success and failure, crossing that fine line.
"The expectation levels are going to be greater because of the progress we made last year, and that's a credit to the players.
"They have to accept that challenge and take it on, as I do and as my backroom staff do as well."
Key elements of that backroom staff were noticeable by their absence when the players reported back to Lennoxtown on Wednesday after their summer break.
But Johan Mjallby and Alan Thompson are due to report for duty today, and Lennon is confident they will soon have the contracts they want.
"They are in talks at the minute, and hopefully that will be resolved by the end of the week or early next week," said Lennon.
"It's important for continuity, and important for me to have people I've brought in and trust, people whose opinion I value, that they carry on working at the club next to me."
Lennon leant heavily on his coaching staff during the dark days after the side crashed out of Europe in August, and admitted that was the point when he questioned whether or not he would be given the chance to continue to lead the team.
But he weathered those storms. And, while it is never going to be plain sailing as Celtic manager – especially one targeted by the worst elements of our society – never for one moment would Lennon consider this was a job he did not want to do.
However, for his enhanced rolling contract to keep on rolling, he knows he must deliver the big prizes.
The SPL title remains the Holy Grail, and Lennon is honest enough to admit the clock is already ticking on him bringing it back to Parkhead.
He does not want to test anyone's patience by failing to win it for a second season."
The Celtic manager added: "Three years without the title is a long time for us and I think it's imperative we do win it from my own point of view," is his summation.
"If you go two years as an Old Firm manager without a title, it might be very difficult to keep your job. But it depends what the season brings.
"The pressure of the job is always the same – win the league.
"If you can win a double or a treble, brilliant. But win the league is a must, really.
"I've had one go at it. The fans might get a bit fed up if I miss out on a second.
"We want to make inroads in Europe this season as well, if we can.
"We've got good natural talent and a good young team. With a bit more experience in there, we feel we can have a go at that as well."
"We will be a year better, and the continuity is important.
"It's important we keep our best players and that is what we will endeavour to do.
"I would like to trim the squad a little bit.
"If I am going to bring a couple in, we will be open to offers for certain players. But I am not going to speculate on them at the minute."