The Northern Irishman is coming under increasing pressure with the team 11 points behind rivals Rangers, albeit with two games in hand.
The Green Brigade released a statement and posed outside of Parkhead with a banner: "save the ten - time to go Neil".
They warned the club’s chiefs that they will be held to account if Celtic fail to win the league and reach ten in a row.
The statement read: "Neil Lennon and many of the current Celtic squad have delivered unprecedented success for our club and deserve enormous credit for their achievements.
"However, past accomplishments are not enough to excuse the level of performance and lack of desire we have endured throughout this momentous season.
"Despite having the best squad in the country, the football on display has been dismal, lacking in ideas and belief.
"Many of our best players have disappointed and we have performed poorly both domestically and in European competition, winning only two games from our previous eight.
"Whilst we would love nothing more than to see Neil Lennon win us the championship, we are part of a growing element of the Celtic support that has sadly concluded that he is unable to turn our season around.
"After a decade of unrivalled footballing and financial dominance it is disappointing to find ourselves 11 points off the league summit and virtually out of the Europa League, having failed to make it past even the second round of qualification for the Champions League.
"We appreciate all that Neil Lennon has done for the club and endured in his time in Scotland. However there is simply too much at stake to persevere in hope rather than expectation, and a managerial change needs to be made.
"Celtic Football Club is bigger than us all and the good of the club must come first.
"Peter Lawwell and the Celtic board must act now in a bid to save 10-in-a-row as well as their own legacies. Should they fail to deliver this title, it will be them who are held to account."