The Parkhead club have had at times an uneasy relationship with the vociferous and political section of the Hoops support, who boycotted Saturday's 6-2 Scottish Premier League win over Dundee United at Parkhead, due to what they claimed to be "the continued police harassment of our members".
The fans' group released a lengthy statement airing their grievances which they say has led to a situation where "any relationship with the club has completely disintegrated".
Within the statement was criticism of Celtic chief executive Peter Lawwell and Hoops boss Lennon for allegedly not addressing their concerns.
The Parkhead club responded with a statement which promised that "each incident or complaint will be investigated" while also saying: "Accusations suggesting that the Club is in some way involved in targeting supporters are ludicrous.
"These accusations have absolutely no foundation whatsoever and, of course, are very disappointing."
Ahead of Tuesday night's visit to St Johnstone in the SPL, Lennon, who has often backed the Green Brigade for the noise and colour they bring to home games especially, was looking for resolution.
He said: "I have had no direct contact (with Green Brigade). We did make an offer to speak to them a while back but they never came forward.
"There is no need for all this unnecessary conflict between any group of supporters and the club because we are moving well on and off the field.
"The club have always maintained an open stance on it, that if anyone has a legitimate complaint the club will look at it and deal with it as best they can and that has never changed.
"They (Green Brigade) are an important part of the club, they have brought an energy and a freshness to the stadium and I have been quite supportive of that.
"However, there is no collusion between the club or any of the authorities to dampen that.
"Our main concern is health and safety within the ground and, as I said, if anyone has a grievance, write to the club, who have helped in the past as best they can and have helped in a lot of ways and that stance remains open to the Green Brigade."
Strathclyde Police are aware of the Green Brigade's complaints but have yet to respond.
While Lennon was conciliatory in his approach to the Green Brigade, the Northern Irishman was unimpressed with reports which claimed UEFA were "irritated" by his threat to send a DVD of complaint about Spanish referee Alberto Mallenco.
The Celtic manager was raging at the official for not punishing severely enough the Juventus players who manhandled his men during the first leg of the Champions League last-16 clash at Parkhead last Tuesday, which the Italians won 3-0.
"I think it is a load of rubbish myself, there is no direct quotes from UEFA so I would disregard that story," said Lennon.
"We may not (send a DVD). We have compiled something but we might just do it through a phone call.
"All I want is clarification. If that is allowed in the game then fine, we will start doing it, or were UEFA happy with the referee's performance and some aspects of the game? That's all."
Lennon revealed skipper Scott Brown will see a specialist to ascertain whether or not he is to go under the knife.
The midfielder sat out the United game at the weekend with an abductor problem and will miss the trip to Perth.
Brown, however, has been bothered by an ongoing hip problem this season which was thought at one time to require surgery, but both problems are to be addressed.
Hoops manager Lennon said: "Scott will be seeing a specialist regarding his abductor and we will wait on the outcome of that.
"We will have a look at what he had before and he might require surgery, we are not sure yet, we will see what the specialist says but hopefully that won't be the case."
Celtic are 18 points clear of Motherwell at the top of the table but Lennon insists complacency won't be a problem.
He said: "We want to keep the run going.
"There has been no signs of complacency, we have our targets to reach and some players might have targets so we are pretty focused."
Strathclyde Police later responded to the fans' accusations.
Deputy Chief Constable Ruaraidh Nicolson said: "We are aware of claims by a specific group of Celtic fans of police harassment.
"We would actively encourage anyone who thinks they have been unfairly targeted to report their concerns to us and be confident that a thorough investigation will be carried out."