The former Hoops shot-stopper – who was given his chance in the Parkhead side by Billy McNeill as a 20-year-old – is convinced it is essential a new No.1 is given time to settle into the side and familiarise himself with his surroundings and team-mates before the serious action starts.
Bonner understands it is not always possible to get the man you want as quickly as you would like, and acknowledges the work which going on behind the scenes to bring in the right player.
But he believes it should be a priority for Lennon, and will be closely watching developments this week as the highly-experienced Stipe Pletikosa and the Belgian, Stijn Stijnen, arrive for medical tests and a trial respectively.
With Shay Given now out of the equation after agreeing to join Aston Villa in a £3.5million deal, and Fraser Forster no nearer to finding a way out of Newcastle, the options open to Lennon are reducing.
And Bonner made no attempt to disguise the fact he believes it would have been beneficial to all concerned if the new No.1 had been signed, sealed and delivered by now.
"I'm disappointed that it's not tied up at this stage," admitted Bonner.
Lukasz Zaluska is in line to start the season at Easter Road this weekend after playing in the warm-up matches in Australia.
But Bonner is concerned that the Pole – who has been at the club for two seasons – has yet to fully emerge from the shadow of countryman Artur Boruc.
He said: "Possibly he still casts a shadow for Zaluska. Boruc was a big character and a different personality. He could handle the odd mistake along the way, and everything else that was thrown at him.
"I don't know what kind of personality this young man has. You see personality during the games. Boruc was portrayed as being very confident, and maybe that's what this young man has to portray.
"It's all about him being a bit more single-minded."
Bonner knows all about the intense scrutiny under which a Celtic keeper must survive and thrive.
With Rangers setting their sights on a fourth SPL title, the pressure will be there from the opening matches.
He reckons this might have a big bearing on the kind of keeper Lennon finally selects, and explained: "If they'd won the league last year, then it would have been different.
"They could have afforded to bring a younger guy in and give him a chance. But this season they've got to win the league, so they may have to bring someone with experience in.
"I was very impressed with the way Neil set his team out and their expansive passing game. Two good full-backs getting forward, which is a Celtic thing, players in the middle who can pass the ball, and pace up front.
"The fans are behind Neil after what he went through, but they will be expecting the league this year. I don't think they can see Rangers getting four in a row."