Lennon and Celtic coach Gary Parker were forced to leave the game early after the Parkhead manager was spat at and verbally abused.
The Celtic staff were seated in the main stand to watch Aberdeen's victory over St Johnstone when fans spat, threw coins and shouted insults at them.
They left after 70 minutes of the game, according to the Celtic manager's agent, Martin Reilly, who criticised the stewarding of the match and called fans' behaviour "scandalous".
Reilly said: "I'm absolutely raging about the treatment of Neil, about the stewarding and the fans' behaviour. It's scandalous that Neil is treated like this."
A spokesman for Aberdeen said such actions would not be tolerated and added that the club is appealing for witnesses. He said: "The support we enjoyed at Tynecastle was absolutely fantastic and helped to create an incredible atmosphere. However, it would appear that a tiny minority within the main stand behaved in a manner that is completely unacceptable and has absolutely no place in football and we would urge anyone who has any information as to the identity of those responsible to get in touch with the club in order that appropriate action can be taken."
During the match, which Aberdeen won 4-0, play was held up briefly as two young supporters ran on to the park and reached the technical area, where Lennon was infamously attacked by a Hearts supporter in 2011.
The pair were quickly apprehended by police and stewards.
During the 2011 incident a Hearts supporter managed to reach Lennon before being pushed to the ground by police and arrested during Celtic's Scottish Premier League match.
A jury returned a verdict of "not proven" in the case of John Wilson, who claimed he had not assaulted Lennon but had slipped and run into the Celtic coach, who was standing next to manager Lennon.
Wilson was charged with breach of the peace but not assault. The incident happened during a season in which Lennon had to be given protection when he was subjected to death threats.
Since becoming a coach for Celtic in 2008 - after a distinguished playing career for the Parkhead side - before taking the helm in 2010, Lennon has been target of assaults and threats, including a bomb threat. Two men were jailed in 2009 for a "vicious, brutal and cowardly" attack on the 41-year-old.
David Whitelaw and Jeffrey Carrigan were each jailed for two years after a jury at Glasgow Sheriff Court found them guilty of punching the former player to the ground and then repeatedly kicking him on the head and body as he lay unconscious.
The attack, in Ashton Lane in Glasgow's west end, happened after the two men mocked Lennon over Rangers's 4-2 win over Celtic earlier that day.
In 2012, Trevor Muirhead and Neil McKenzie were convicted of conspiracy to assualt the Celtic manager, the late QC Paul McBride and ex-MSP Trish Goodman between March 1 and April 15, 2011.
Speaking in a radio interview in 2012, Lennon admitted that he had thought about leaving Scotland, saying: "You're thinking, is it worth living here?" During the bomb trial Lennon had told the court he was left "very disturbed" after learning that he had become a target, along with other prominent fans of the club.
Lennon was close friends with McBride, who died on a trip to Pakistan in March 2012, days before he was due to give evidence in the case.
The Celtic manager and former club player, who was a pall-bearer at McBride's funeral in Glasgow, said losing his friend coupled with the stress of the case made for a "tough spell".
In the radio interview he added: "I had a real difficult time when Paul McBride passed away. And there was a spell where, on the Monday, it was Paul's funeral and then on the Tuesday I had to go and give evidence in the court. That was a real tough, tough spell."