Lennon eased some of the pressure on his shoulders on Sunday with Celtic’s 4-1 win over Motherwell at Fir Park, but Rangers then drubbed Hamilton Academical 8-0 later in the day to re-establish a nine-point lead.
Celtic do have two games in hand on Rangers, but Dalziel thinks the nature of a pivotal season means Lennon is not far from the exit door given how Steven Gerrard’s men are playing.
He feels that, while unfair, two league defeats would mean the end of the road for Lennon.
“I don’t expect Rangers to go through a full season like this, but they are going great guns, not losing goals, they are scoring goals, have a way of playing that is working for everyone”, Dalziel said on Radio Clyde Superscoreboard.
“If Neil Lennon was to go and lose two league games…I think Neil Lennon is in a situation where it is [lose] two league games and you are out, I really do.
“I think it is unfair, but I think it is the nature of the beast this season.”
Lennon shrugged off criticism around Mohamed Elyounoussi on Sunday to start him at Motherwell and the forward repaid his manager by grabbing a hat-trick.
The Celtic boss will now be crossing his fingers for his key men to remain fit over the international break.