Lennon has picked up on the sense of expectation and even celebration among the Celtic support given that the club remains on course for a domestic treble while Rangers appear to be heading towards administration. The Celtic manager has downplayed talk of winning the Clydesdale Bank Premier League, William Hill Scottish Cup and Scottish Communities League Cup and was unimpressed by headlines on Adam Matthews' quotes yesterday which alluded to Celtic being invincible for the rest of the season.
But Lennon cannot govern how fans feel about what may happen in the coming weeks – at Parkhead and at Ibrox – and wants his players to remain detached and professional.
"We cannot affect or take in what is going on across the road [at Rangers]. People will be coming up to the players, slapping them on the back, thinking the league is over and all that sort of rubbish. But we've got to keep everything in house and concentrate on what we're doing game by game. We are only a point ahead with a game in hand. And that can change very, very quickly."
After two cup ties, Celtic return to league duty against Hearts at Tynecastle this evening, and they will attempt to extend their 15-game winning run in domestic fixtures. "Adam created some headlines, which I wasn't happy about," said Lennon. "Looking at his quotes they weren't too bad, but even if we do go unbeaten in the league there's no guarantee we'll win the title. It could be seven wins and seven draws, and that might not be enough. So it's far from over.
"The players are proud of the record they are on at the minute and there is a real incentive for them to keep that going. They should be self-motivated because a few of them will remember the hangover from last year and they should want to go one better. It's the same with the League Cup. And they'll want a go at the Scottish Cup again.
"You don't get anything given to you, and you can't listen to outsiders speculating on what is going to happen either here or over there [at Rangers]. You have to maintain your focus like all the good teams do."
Lennon admitted it was true that some supporters were effectively celebrating already. "Absolutely, but the players are not fans. Some of them will have an affiliation with the club, obviously, but the main thing is they are professional footballers. While this run goes on, there will be a team lurking out there that wants to take our scalp. A lot of outsiders will want us to fall. That is the challenge which lies ahead."