As keeper Fraser Forster entered the record books by beating Charlie Shaw's shut-out record of 11 league games, the champions moved 21 points clear at the top of the Premiership with victory over St Mirren on Sunday.
Aberdeen visit Parkhead this weekend as Lennon's side look to keep their dreams of a domestic double alive and defend their Scottish Cup crown.
A rare off night against Morton saw them crash out of the League Cup earlier this season and the boss knows there can be no complacency as they bid to extend their superb recent run.
Lennon said: "Winning games and going on a run like this is a very difficult thing to do.
"You only have to take your eye off the ball once and it comes to an end.
"If you have three or four players having an off day, like we did against St Mirren in the semi-final last season, then it costs you the chance of a treble.
"While we are on this run, we are always walking on a tightrope because someone can bring an end to it at any time.
"We give the players reminders of what we are trying to achieve here and looking at the progression, both as individuals and a team, to where we want to be.
"We always remind them of the Champions League campaign.
"We realise how far we have to go to be in that company on a consistent basis."
While Celtic are closing in on Premiership glory and have another Scottish Cup medal fixed firmly in their sights this season, Aberdeen are also on the search for silverware as they continue their resurgence under boss Derek McInnes.
The Dons booked another Parkhead date, this time in the League Cup final against Inverness Caley Thistle, with a 4-0 win in their last-four clash with St Johnstone at the weekend.
McInnes' side currently lead the chase to finish best of the rest behind champions-in-waiting Celtic this season and bolstered their attacking line with the capture of Adam Rooney during the January transfer window.
Celtic emerged 3-1 winners the last time the teams met at Parkhead and Lennon knows the Hoops face a stern test on Saturday.
He said: "It is a huge game for us. Aberdeen are obviously on a high after winning on Saturday and getting into the final.
"It is the top two teams in the league and we couldn't have got a tougher draw. It is a game we are all looking forward to.
"We want to defend our trophy. We want to remain undefeated for the rest of the season."