Goalkeeper Fraser Forster kept his 13th consecutive Scottish Premiership clean sheet in a 2-0 win against Hearts on Saturday, breaking former Aberdeen goalkeeper Bobby Clark's 43-year-old league record by stretching his shut-out period to 1,215 minutes.
The victory, which came courtesy of a first goal for the club for Leigh Griffiths plus an injury-time strike by Teemu Pukki, was Celtic's 15th consecutive win in the league and gives them 12 games left to achieve an undefeated campaign.
Celtic and Rangers both achieved the feat in an 18-game season in the late 19th century but Lennon's team would be breaking new ground if they were to do it this season.
Lennon helped Celtic get close 10 seasons ago when Martin O'Neill's team got to the 33rd game of the season before losing their unbeaten run thanks to David Zdrilic's last-minute winner for Aberdeen at Parkhead.
Celtic won 25 games in a row during that run and Lennon wants his side to keep pushing for an invincible campaign to make up for their cup exits.
"It may be a step too far but it's something that is really motivating the players and ourselves to try to achieve," he said.
"That's 26 now, and now we look forward. There is plenty to play for still and that's what is motivating us all."
Lennon knows they face one of their toughest tests on Tuesday when they play second-placed Aberdeen at Pittodrie. The Dons are fresh from defeat by Partick Thistle but they triumphed 2-1 at Parkhead earlier this month in the William Hill Scottish Cup.
"It's fantastic consistency and we are going to get tested again on Tuesday at Aberdeen," Lennon said. "That's a great game to go into and we will look forward to that on top of another productive day.
"They are playing very well and played very well at Celtic Park when they beat us a couple of weeks ago. They are the only team to score against us in the last couple of months so I think the players will be looking forward to that challenge."