Enjoyable though the Glasgow club's first Scottish title win in four years was, there can be no dwelling on success in Lennon's position.
Bringing in a cultured and dominant centre-half, for the umpteenth season running, is a priority for the Irishman in the close season.
A goalkeeper, a left-sided midfielder and a striker are all fairly high on his shopping list in the weeks ahead as well.
On top of that, keeping key first-team players like Fraser Forster and Gary Hooper at Parkhead is also of utmost importance to Lennon.
Yet, the Hoops boss is not now, and never has been, solely focused on bringing in players from other clubs and countries to improve his team's performances on the park.
No, he is always keen to promote the youngsters who are emerging thick and fast at the club's training complex outside Lennoxtown – and has enjoyed some noteworthy results doing so.
James Forrest has been nothing short of a revelation in the last nine months or so and deservedly scooped every Young Player of the Year award going this month.
Elsewhere, Dylan McGeouch and Tony Watt have also impressed greatly during the game time they have been given and look set to be highly effective top-team regulars in the near future.
The six kids Lennon handed debuts to in the Adam Drury Testimonial against Norwich City at Carrow Road on Tuesday night will also give him food for thought.
Stuart Findlay, just 16, started at centre-half alongside Kelvin Wilson and played impressively for the full 90 minutes against the Barclays Premier League club.
Denny Johnstone, Lewis Kidd, Jamie Lindsay, Paddy McNally and Bobby Thomson all came on in the second half to make their bows in Celtic colours.
"I have got plenty of work to do in the weeks ahead before the new season starts," Lennon admitted. "It is major part of my role.
"I enjoyed the day when we were finally presented with the trophy for winning the league. But as soon as the festivities were over I started looking ahead to the new season, planning for the next campaign. We are working away.
"Of course, we have to reduce the size of our squad as well as strengthen it. We will, therefore, be attempting to move on some personnel in the close season as well as taking new players in. But not much surgery is needed. We are happy with the players we have."
He added: "But I am well aware that we have also got many gifted young players emerging from our youth ranks.
"Anybody who was down at the Norwich game saw the strength in depth we have, saw that we can call on the youngsters and be confident they can do a job for us.
"They played against a team that has performed extremely well in the Premier League this season and they didn't look fazed by the experience at all.
"Yes, of course, we would like to bring in two or three quality players over the summer, but I think the Norwich game underlined that the club is in a pretty good state at this moment in time."
Watt, the teenage forward who netted a debut double against Motherwell at Fir Park last month, started in Norfolk and performed brilliantly out wide.
That Watt, along with Forrest, McGeouch and others, continues to impress, underlines how well youngsters are managed when they make the breakthrough into the senior side.
So, don't be at all surprised if the 18-year-old, or one of his contemporaries, features as much next season as any of the big-money summer signings Lennon succeeds in luring to Celtic.