But strengthening the spine of the team is the essential surgery required ahead of next season if the Hoops are to stand up to the rigours of defending their SPL title and making inroads into Europe.
The goalkeeping situation is still up in the air as Lennon attempts to tie down Fraser Forster on a long-term deal. The giant 24-year-old is the man the Parkhead boss wants, but personal terms remain to be agreed.
Lennon knows he must have alternatives up his sleeve and with Craig Gordon set to be released by Sunderland, pressure may be exerted to get Forster's agent at the table to determine if the man who has been at Celts on loan for the last two years is now prepared to commit for the next four.
A powerful central defender, preferably an experienced one, is another must for Lennon and the way has been cleared with the departure of Glenn Loovens, Daniel Majstorovic and Darren O'Dea.
Leicester's Matt Mills is one target. But again Lennon has several irons in the fire after collating all the reports from his scouting team.
A striker who can capitalise on the service from the wide areas, particularly when the ball is delivered in the air, is another high priority.
But, of course, such men come at a premium, so others may have to leave to pave the way for arrivals.
With midfield the best furnished of all the departments in the side, there is room for movement there, and Ki Sung-Yueng is already earmarked as potential saleable asset.
Former Celtic keeper Pat Bonner has been a keen student of the transformation Lennon has brought about over the past two seasons, and he would add a creative midfielder to the shopping list already defined.
The ex-Republic of Ireland star recognises it is also vital Celtic hold on to the quality players they already have, with the likes of Gary Hooper already a target for Premiership clubs. He said: "They were lucky last year to move Aiden McGeady on for £9million. Celtic are no longer a team that can hold on to all their talent."
HE ADDED: "If someone comes in with a ridiculous bid, they may have to sell to finance the restructuring of the team. But I'm sure Neil wants to keep a 29-goal striker. That takes a lot of money to replace."
Hooper was a vital cog in the Green Machine that drove Celtic back to the top of the SPL, but Bonner reckons the hard work has only just begun. He said: "Winning the league has sent out a message to everyone that Celtic are back, and I think Neil has built a really good young squad.
"He'll have to add a couple, and move a few out. Fans will demand success in Europe, and it's hugely important to get through the qualifying rounds.
"Neil knows he has the backing of the supporters and the board, but the hard work starts now.
"He has an enormous squad, so he'll need to trim before he can add. Celtic no longer have the huge reserves to go out and spend £10m or £15m.
"I'm sure he knows who he'd like, but I'd like to see someone in the middle of the pitch who can go and pass really good balls for people making runs.
"They possibly need a striker, too, someone who can take the weight off Hooper, while playing alongside him.
"And if they want to be effective in Europe, they may need to get a player who has real character and the ability to play out from the back."