The Hoops moved 20 points clear of rivals Rangers on Wednesday when they defeated Dunfermline 2-0 thanks to goals from Charlie Mulgrew and James Forrest.
The win was Celtics 16th in a row in the SPL - a run that extends back to November 6 when they defeated Motherwell - and their 19th consecutive victory in all domestic games.
With a place in the League Cup final and a semi-final spot in the Scottish Cup already secured, Celtic remain on course for a treble while Old Firm rivals Rangers, who were docked ten points after entering administration last week, continue to fight for their financial survival.
And Celtic boss Lennon, who was part of the Martin ONeill side that won 25 matches back to back in the 2003/04 season, has urged his side to continue their winning run as long as possible as they look to close in on their first title in four years.
"Dont spoil it. Dont let the run get away," Lennon said.
"Something like this happens maybe once in your career and they should be proud of it and try and hold on to it for as long as they can. Thats all Im asking them to do.
"They could easily have switched off against Dunfermline but they didnt and Im delighted with that.
"Weve got another big game against Motherwell on Saturday and they are going for second place now so it will be a huge game in the context of the league.
"Then we have got a couple of big cup games coming up on the horizon as well so there is a motivation to keep this run going and there is a motivation to play in these games.
"This is a young team and for all intents and purposes we havent spent a great deal of money on putting this squad together. But theyve been a credit to the club and Im very proud of them.
"They have kept this winning run going and opened up a huge gap in the championship and I cant really ask any more of them."
The Hoops will face a Motherwell side who are undefeated in their past six league matches. Stuart McCalls side are on a high after coming from behind to record a 4-3 win over Hiberian on Wednesday and could draw level on points with Rangers in second place with a win over the Hoops.
Crisis-stricken Rangers are not in action until Sunday, when they face a difficult away trip to Inverness.
The clubs problems off the pitch are being mirrored on it with a long injury list including Kyle Lafferty, Steven Naismith, Steven Whittaker and Jamie Ness while Sasa Papac is suspended after his sending off against in the defeat to Kilmarnock last weekend.
Striker David Healy has urged the fans to stick behind the team during a difficult time for everyone at the club.
"One thing we will do is stick together. Its all about staying strong in these testing times," the Northern Ireland international said.
"Weve all got families and livelihoods but we'll get through it Im sure, especially with the fans we have. They are magnificent."
Fixtures (1500 GMT unless otherwise stated)
Saturday
St Mirren v Aberdeen (1200)
Celtic v Motherwell
Hearts v Dundee United
Kilmarnock v Hibernian
St Johnstone v Dunfermline
Sunday
Inverness CT v Rangers (1245)
Source: AFP
Source: AFP