Lennon was widely criticised for his actions at the end of the Old Firm derby last week, where he clashed with the Rangers assistant manager, Ally McCoist. It subsequently emerged that a suspicious package – made out to look like an explosive device – addressed to Lennon was intercepted by police.
The Celtic manager is under 24‑hour security surveillance after bullets were also sent to him and further threats were made towards his life.
"Neil reacted to a particular situation he didn't instigate in a way which he regrets," said Lawwell of the McCoist affair. "He immediately apologised to the board and the matter is now closed. He also met with Ally McCoist. We do not condone his behaviour. He agrees he slipped below the very high standards set at this club.
"In terms of mitigating factors you need to understand what is going on his life. He is man who is under the normal pressure as Celtic manager to win games. But other than that he's got to put up with live ammunition being sent through the post, death threats, 24 hour surveillance and security measures. So it's quite a lot to take on at the moment."
Martin Bain, Lawwell's counterpart at Rangers, said there would be no ongoing issue between the Old Firm clubs on account of last week's Scottish Cup tie. "That was a week ago, we have moved on," Bain said. "As clubs, that issue has been dealt with internally."
In response to the suggestion of direct allegations being made against Lennon or Celtic, Lawwell added: "We try and operate with the highest possible standards. The reputation of Celtic is something we hold dear and if someone tarnishes that, action will be taken."
It was confirmed after a three-hour summit featuring Celtic, Rangers, Scotland's first minister and Strathclyde police that players from both halves of the Old Firm will receive a training-ground briefing from officers before they meet in the League Cup final on 20 March.
Stephen House, Strathclyde police's chief constable, said: "In reality, we don't think that having a police officer in a dressing room three minutes before kick-off would make much of a difference to players. What we have think would be better, instead, is an in-depth briefing to explain to players what the law is."
House stressed that any sense of players or coaches being arrested for bad behaviour was "a last resort beyond all belief".
Talks will take place before the start of next season regarding Old Firm scheduling. The police would prefer the Glasgow derby to routinely take place on a midweek night, a suggestion both clubs are uncomfortable with.
Beyond that, the police have promised to hand out stiffer punishments to fans who produce threatening or sectarian remarks on internet forums. "It is not legal and it is not tolerable in Scottish society," said the first minister, Alex Salmond, of website abuse.
guardian.co.uk © Guardian News and Media Limited 2010