Lawwell confirmed last week that he will retire from his post as the club’s chief executive at the end of the season with Scottish Rugby’s chief operating officer Dominic McKay set to take his place.
His departure followed a series of fans protests against the board in the wake of the club’s failure to mount a serious challenge for a record-breaking 10th consecutive title.
Lennon’s position has also come under severe scrutiny following a disastrous run of form since October that has seen Celtic fall 23 points behind Rangers, while also crashing out of the Europa League and the Betfred Cup.
However, Lennon stated: “Why would it be my intention to go? Peter’s decision has nothing to do with my position at all, or my coaches or any of the players. So I don’t understand the context of the question at all.”