Lennon is looking for a similar outcome when he returns to Tynecastle with the Hoops for the first time since he was attacked by a Hearts fan there in May - but only in terms of his side's performance.
Celtic's comprehensive and impressive 3-0 win was completely overshadowed by the touchline incident which saw the Hoops boss accosted by an irate Jambos supporter who had emerged from behind the dugout.
During his trial John Wilson admitted attacking Lennon but the charge of assault, aggravated by religious prejudice, was found not proven although he was found guilty of breach of the peace.
The Northern Irishman, who joked that he will have his burly assistant Johan Mjallby minding him in the technical area this time, is looking for his players to keep on the heels of SPL leaders Rangers by finding the form of that eventful night in Gorgie.
"We have had some decent performances since but have not really hit the heights of what we know we are capable of and I think it is only a matter of time before we do," he said.
"All I'm concerned about is trying to win the game and for the team to play as well as we can.
"I am hoping the Tynecastle episode was the tipping point and we can get back to discussing football matters.
"I also just hope both sets of supporters behave themselves as well as they can and we are talking about the game and the atmosphere in a lighter note rather than the last game.
"I watched Hearts lose against St Johnstone last week and by their own standards they were disappointing.
"But when we come to Tynecastle, it is always quick and physical and the atmosphere adds to that as well and they always put on a strong performance against us and I will expect no different."
Celtic fans can expect changes to the team which drew 1-1 with Udinese at Parkhead in their Europa League Group I clash on Thursday night.
However, Lennon refused to reveal whether keeper Fraser Forster will return after being replaced by Lukasz Zaluska for the visit of the Italian side.
"I put Lukasz in just to freshen it up," he said.
"He is training really well. We have had a lot of games recently and it will keep Fraser on his toes as well.
"We have good competition in that position."
Lennon maintained his staunch backing of his much-maligned striker Georgios Samaras who elicited moans and groans from the Celtic fans when he came on as substitute against Udinese.
The former Celtic skipper said: "I do feel for him a little bit but he is a big boy and he has a good temperament.
"Whenever any player goes through sticky patches or gets any grief from the crowd, he has to win them over.
"He's just got to work hard in training, keep catching the eye and when he gets the opportunity, go and show people what he can do.
"We know he has good attributes. We know we are not seeing them at the minute but we know we have a good player there."