The Parkhead club have won the last 10 trophies available in Scotland and are going for nine league wins in a row this season while hoping to clinch a domestic quadruple treble.
However, Rangers' 2-1 win at Parkhead at the end of last year took Steven Gerrard's side to within two points of the champions with a game in hand, giving added hope to the Ibrox side of ending the domination of their Old Firm rivals.
Asked if he thought suggestions that a changing of the guard might be hasty, the Celtic boss said: "I think it is very premature, yes.
"Looking at the league table I think we are still top of the league even though they have a game in hand.
"We won the (Betfred Cup) and up until then (the defeat to Rangers) we had won 11 (league) games in a row.
"So we are very positive about the second half of the season.
"So look, I can't control what other people think. You expect it sometimes off the back of a defeat but a lot of people over the years have been proven wrong."
Lennon expects his squad's winning mentality to play its part over the run-in.
"That experience might stand them in good stead but every season is different," said the former Celtic captain, who revealed that Ivorian midfielder Ismaila Soro is undergoing a medical in Israel as he waits for a visa to be sorted to confirm his move from Bnei Yehuda.
"We have a good, strong, core of players in there who are winners and they won't want to give anything up lightly as we have seen already.
"So the second half of the season should be exciting.
"Killie are a tough nut to crack. There has been a change of manager twice and I think Alex Dyer might go back to the way they played previously.
"We are away from home, we know the venue is tough, we know the artificial surface isn't always conducive to playing the style of football that we like but we are aware of that so it will be difficult but it is one we are looking forward to."