The atmosphere on Celtic's excursions there can be distinctly poisonous, not least on the night Lennon was attacked as he stood on the touchline during a match in May last year.
But the Northern Irishman feeds off the adrenalin that pours down from the steeply-banked stands in Gorgie and is genuine when he says the loss of the Hearts-Celtic fixture, at the same time as the Old Firm match, would have dire consequences for the Scottish game.
Hearts face extinction unless they can pay an outstanding tax bill of £450,000 by next weekend. Lennon hopes a way can be found to rescue them from crisis. "I hope it is not the last [game between the sides] ever, because despite the incident a couple of years ago I like Tynecastle as a venue," the Celtic manager said.
"With it being a midweek game as well it will be a wee bit more electric in the atmosphere. It is bad enough losing Rangers but to lose probably the third-biggest club in Scotland would be nothing short of disastrous really. So I am hoping they can get through the problems they are going through at the moment and come out the other side."
Lennon sat alongside Hearts manager John McGlynn at the Scottish Football Hall of fame dinner a fortnight ago, and expressed his sympathies.
He has been impressed by the rebuilding job performed by the former Raith Rovers manager after the likes of Craig Beattie, Rudi Skacel, Ian Black and David Templeton were lost to the squad. Young striker Callum Paterson, in particular, has caught Lennon's eye.
"It was probably the last thing he wanted to talk about," Lennon said. "He is a great football guy, he has just inherited the club at probably the wrong time. When you consider the job he did at Raith, to be going through this must be tough for him."
The Hearts players rarely seem to let the club's financial trouble affect them, but the sense of occasion may also serve to lift the visitors.
Celtic may have struggled to lift themselves for some league games this season, but last Saturday's 2-0 victory over Aberdeen in front of a near sell-out crowd at Pittodrie underlined the fact they also seem to thrive amid adversity.
"I am hoping the atmosphere will be good and it will heighten the senses of the players," Lennon said.
That atmosphere may remain unchanged from past years, but the two clubs no longer compete on a level playing field. There have been changes aplenty in the Hearts side even from that which knocked Celtic out of the Scottish Cup at the semi-final stage last season.
McGlynn, who was appointed after Paulo Sergio's departure in the summer, admits the fiscal gap between the teams is widening, but, as the Parkhead side showed against Barcelona, that does not make the more well-off side invincible.
"The stage they're playing on is where they want to be and they've done exceptionally well on it – better than some of us might have imagined given they might have had to cut back a bit with losing Rangers," McGlynn said.
"And because of that, they're making more money, getting points in the Champions League and creating even more money. So you can only see the gap getting wider.
"It's not rocket science – if you spend your money wisely you have the opportunity to bring better players to your club and enhance your team further. It helps Scottish football gain respect, it helps the co-efficient, but the gap could keep growing because of it."
While Hearts have thrown their focus upon youth, it must also be galling for managers such as McGlynn to know Celtic also have much of the best young talent in the land on their books, such as Tony Watt.
Jason Holt, a highly-rated young midfielder who has made an impact in the Tynecastle first team in recent weeks, is looking forward to renewing acquaintances with the striker, a Scotland Under-19 squad-mate he has locked horns with in many a Hearts-Celtic youth team clash.
"I know Tony from Scotland trips we have been on and we are quite good friends," Holt said. "He's always managed to score so I wasn't surprised to see him burst on the scene and bag the goals he has done. I am happy for him that's he's doing so well."
This new mutual appreciation society between east end of Glasgow and west end of Edinburgh will be suspended at around 7.45pm on Wednesday night.