The Hoops boss does not want any kind of shock cup exit to undermine the momentum being built up by the club in the run in to 2013.
Lennon's icy blast included a demand that the right attitude is taken to freezing Gayfield.
The Irn-Bru Second Division side hope to use the anticipated windy conditions and bumpy pitch to go one better than they did at Parkhead, where the held the Hoops to a 1-1 draw.
The live Sky TV game and full house guarantees a bumper pay day for the Red Lichties.
But Lennon wants that to be all they have to celebrate, and is ready to unload all of his big guns tomorrow night. He said: "We will go with a strong team and make sure we can progress.
"But it's going to be difficult. It will be another cup final for Arbroath, so we are going to respect them and respect the competition.
"We want to proceed in all the competitions, and tomorrow will be no different."
"Look, I know from over the years that anything can happen," added Lennon. "Yes, it will be cold. It might be windy. It might be a difficult pitch to play on. So, we will have to pick a team to suit the conditions as well."