The Bhoys will lock horns with Saints in Sunday's Scottish Communities League Cup semi-final.
The Parkhead men are overwhelming favourites to win at Hampden against a struggling Buddies side who have failed to win a point or even register a goal in their last eight meetings with Celtic, while losing 22 goals in the process.
Northern Irishman Lennon has suffered two Scottish Cup semi-final defeats, to Ross County and Hearts, since he has been in charge of the Hoops.
Moreover, this week he watched League Two side Bradford overcome Aston Villa over two legs to reach the Capital One Cup final, where they will meet Swansea who won through against highly-fancied Chelsea.
And it was those matches which Lennon used at the club's snow-bound Lennoxtown training complex today to knock down talk of an easy passage through to the March final.
"People make big issues of records and the longer it goes on, the more people talk about it, until it's broken," he said.
"It can go any time and I am very wary of St Mirren, I am very wary of it being a semi-final at a neutral venue.
"Did you see Bradford during the week? And Swansea knocked out Chelsea and had two clean sheets so anything can happen on any given day and whether it be St Mirren or Ross County, who beat us before in the semi-final, they are games that we can't win.
"If we win it, we are expected to win, we lose and it is a big cup upset. That's why I am wary.
"We are walking on a tightrope and if anything goes wrong our dreams of winning the treble will evaporate in one game, so we need to be very careful."
St Mirren boss Danny Lennon was criticised in many quarters for his defensive tactics in the 2-0 SPL defeat by Celtic at Parkhead in December.
However, the Hoops boss stuck up for his namesake.
"It is unlike Danny but he has to do what is best for his team and club," said Celtic boss Lennon.
"He took a bit of flak for it but he is not the first manager to do that.
"Different managers will have different ways of approaching us and that is their prerogative.
"There is no criticism coming from me, we have to find a way to work it out.
"So I thought the flak was totally unjustified because, if anything, Danny is a forward-thinking manager and is quite flexible with his tactics.
"He has St Mirren playing an attractive brand of football, albeit results have not been going their way.
"But if they find a bit of consistency in the second half of the season they could make the top six.
"Whatever tactics they adopt on Sunday, though, we have to try to find a way of overcoming them."
Lennon revealed it was "as you were" with regards the future of 22-goal striker Gary Hooper.
Celtic rejected an improved offer from Norwich for the 24-year-old striker in midweek, with the original bid reported to be £5million.
Former Celtic skipper Lennon said: "I made my feelings pretty clear in midweek. He is our player and we want him here.
"I think he is playing wonderfully well and I even think there is more to come from him which is good. I think he is going to get better and better."
Lennon revealed why Sierra Leone striker Mo Bangura left Celtic to join Swedish side Elfsborg on loan.
He said: "We have a lot of strikers here and it is an opportunity for him to play regular football, which he wouldn't be guaranteed to do here.
"So it makes sense for both clubs."