Saints reached their second Scottish Communities League Cup final in four years by beating Celtic in the semi-finals last month.
In doing so, they overturned a run of eight successive defeats against the Hoops in which Saints had been outscored by an aggregate 22-0.
They now face the Glasgow giants once more on Saturday hoping to cause a second upset by knocking the SPL leaders out of the William Hill Scottish Cup.
And Lennon is hopeful of his team's quarter-final prospects.
He said: "Our performances in my time here against Celtic before that semi-final were not great, not scoring a goal, never mind winning a game.
"So we know we need to be at our best.
"A lot of people have written us off already. A lot of people have asked if lightning can strike twice. My answer is why not?"
Meanwhile, Lennon has warned whoever takes over at League Cup final opponents Hearts to be "very careful" about what they are getting into.
The Tynecastle club yesterday parted company with manager John McGlynn after his side were shot down 2-0 by Lennon's men in Paisley on Wednesday night.
The defeat leaves Hearts sitting second bottom of the SPL but Lennon claims the former Raith Rovers boss was doing a good job under severe financial restraints that had already seen many of Hearts top earners depart.
He said: "It's disappointing because I don't think John got enough credit for the difficult job he had at Hearts.
"It's a club that is going through financial strains at this minute in time but when your club suffers and your results suffer, it is the manager whose head who is on the line.
"However, I thought he was doing a terrific job. There's a lot of kids that are getting valuable experience and that is only going to set Hearts up for the future.
"But we've been through this ourselves. Bleeding younger guys in, you are going to get that inconsistency and hit lows."
McGlynn was the ninth man to be given the job of managing the Gorgie club on a full-time bases since owner Vladimir Romanov bought Hearts in 2005.
But Lennon - whose side will face the Jambos again at Hampden on March 17 - is wary about just who will want to be the 10th.
"There have been many there before John, prior to him getting the job," he said.
"I don't like speaking about other clubs but looking at the amount of managers Hearts have been through these past number of years, any future employee has got to be very careful and do their homework first."