The Parkhead side have won the last seven domestic trophies in Scotland - all of them under former manager Brendan Rodgers, who left for Leicester City in February - and are closing in on an unprecedented treble treble.
If Celtic get past Derek McInnes’ Dons side at the national stadium on Sunday they would face either Hearts or Championship outfit Inverness, who play on Saturday, in the final next month.
The holders go into the game 11 points clear of Rangers at the top of the Ladbrokes Premiership and needing just two wins to guarantee an eighth-successive title win as their stranglehold on the Scottish game shows no sign of weakening.
Interim boss Lennon said: “It is the most important game because it is the next one and that is really the mantra.
“We know everyone outside of the club would like to see us lose that domination so that is the incentive for the players, the extra motivation if you want to call it that, to keep prevailing and keep coming through these really stiff tests.
“I don’t know about extra pressure but there is a lot of talk about that (treble treble) and it is not going to go away.
“They are experienced enough, they have done the double treble.
“Can they do the treble treble? They have four games to do that and it won’t be easy.
“The closer it gets the more difficult it becomes and the expectation and anticipation builds I suppose - but they have handled it pretty well.
“Aberdeen is a key game because it is the next one. Obviously it is a cup competition and it is one-off and we know if you lose that’s it, that’s why it is key. Whereas in the league, you can afford a defeat and still go on to win that.”
The former Celtic skipper hailed the club’s remarkable cup record over the past two-and-a-half seasons where they have yet to be overturned.
He said: “Fantastic consistency and mentality as well and I am just looking for more of the same come Sunday.
“It is more important for the players really. The know they are one game away from another final.
“They have handled these occasions pretty well over the last few seasons and obviously the cup record is spectacular.
“It is important we approach the game the right way. We know we are up against a very tough opponent.”