The two teams will get it on again in the quarter-final of the William Hill Scottish Cup, with Saints landing home advantage.
The Paisley men's 2-0 victory over St Johnstone put them in their sixth quarter-final in two-and-a-half seasons under Lennon as they bid to set up another trip to Hampden.
He said: "Already we are being written off and that suits us just fine. We are under no illusions that Celtic are a quality side and know just how tough this will be.
"But we can take enormous self-belief from our victory over them in the League Cup semi. We know that if we play to our best and maintain the standards we have set in that game we will give ourselves a chance.
"The Scottish Cup is the oldest cup competition there is and we want to go as far in it as we can. We enjoyed our day out at Hampden last week and we want to be there as often as we can.
"So this tie will challenge us to prove we can repeat the standards we set at Hampden a week past on Sunday and we know that Celtic will feel they have a point to prove.
"All in all, it should be a cracking tie and it is great for us that it's at St Mirren Park."
Looking back on the latest cup triumph, Lennon lauded his players for their consistency.
The Buddies rounded off a dream week which had started with the Scottish Communities League cup semi-final victory over the Hoops, and then a three-point SPL haul against Inverness, with this impressive defeat of St Johnstone.
Lennon said: "It has been a fantastic week for us. Over the last couple of months the boys have been really consistent for me with just the one slip-up against Ross County.
"The lads are getting their reward for all the hard work they are putting in.
"But I feel I have to make special mention of Craig Samson in goal for us because he kept us in it in the first half.
"At the other end, Esmael Goncalves has made a fantastic start to his St Mirren career and his goals ultimately booked our place in the quarter-finals."
It did not take long for Goncalves to pick up where he had left off against the Hoops.
With 10 minutes gone the Portuguese hitman slalomed into the Saints box only to be thwarted by David McCracken.
Saints' Geordie midfielder Conor Newton then saw his 25-yard drive saved by Alan Mannus as the Buddies upped the ante.
But it was Samson to the rescue when the Saints No.1 produced an outstanding stop to deny Rowan Vine's powerful header.
The visitors should have gone ahead on the stroke of half-time when Gregory Tade played in Steven MacLean but, with only Samson to beat, he rifled over.
The Perth side were made to pay for their profligacy just after the break when, in 49 minutes, Gary Teale's inch-perfect cross from the right wing located Goncalves and his six-yard header beat goalkeeper Mannus all ends up.
Six minutes later Goncalves struck with his fourth goal in three games for the Paisley men.
The striker held off McCracken's challenge before swivelling snake-hipped to lash a low strike past Mannus.
There was to be no way back for Steve Lomas' men as the Paisley Saints went marching on to yet another quarter-final and added to their burgeoning reputation as cup specialists.