Despite a runaway lead at the top of the SPFL Premiership as he closes in on his fourth top-flight title, the Northern Irishman revealed that his shelf life at the club has been a subject of much internal soul-searching.
He has even sounded out former Celtic manager Gordon Strachan on the subject. The Parkhead boss - despite winning his second successive manager of the month award this week - has come in for intense criticism from his own fans in the wake of last Saturday's fifth-round defeat in the William Hill Scottish Cup to Aberdeen.
And he admitted he wonders whether he can take the team any further forward. Should he remain at the club until the end of next season, Lennon would become the longest-serving manager of the club since Jock Stein - longer than his mentors, Martin O'Neill and Strachan.
"I think you know instinctively when there is a cut-off point," said Lennon. "Whether mine is here yet or not I do not know. I speak to Gordon about it, but it's not high on my agenda at the minute.
"This is a great job and there's a lot of other managers out of work and I don't fancy looking at wallpaper and carpets and stuff like that for the next however long it will be, because once you are out of a job it's very difficult to get back in.
"One, it is good money," he added. "It pays the bills and keeps the clothes on the kids. Two, you can be forgotten about very quickly in the game and that's important to remember as well.
"There are good managers who have been out of the game for two and three years and applied for jobs everywhere and can't get back in.
"You've got to be careful. I'm not saying I'm going to leave here and walk straight into another job. I haven't made any designated plans for that either. I'm not in any rush just yet. It's a huge job and it's like everything else, you have good days and bad days.
"The good days are good and the bad days are horrific. That's part of the excitement as well - you have to be a bit of a masochist to do this job."
Unlike his predecessors, of course, Lennon has to deal with a support which regards the league title as a bare minimum.
"We are going to win another championship by the looks of it and people will go, 'so what?'," said the Northern Irishman, whose Celtic side host St Johnstone today.
"That's a difficult thing to deal with. Years ago, there was a spell where people would have chopped your right arm off for the opportunity to be challenging for a title rather than going on to win one.
"The criticism always outweighs the praise I think.
"There's an apathy at times, people take it for granted that we are going to steamroller everyone.
"Maybe they have a right to expect that because the form we have shown in the last two months has been sensational really. It was going to come to an end someday."