The Blues boss watched his side slump to a record of one win in six following their defeat at Stamford Bridge, leaving them eighth in the Premier League table.
It also marked the first time since August 2017 that Chelsea have conceded three first-half goals in the league, leaving them four places and two points worse off than their position after 17 games last year.
With expensive talents such as Timo Werner and Kai Havertz failing to make an impact this season, it has seen the manager face questions over his position from pundits.
And the Blues faithful have now turned on their former midfielder after the latest defeat to City.
“Lampard out - the guy is clueless,” one supporter said.
Another commented; “Lampard has turned beasts like Werner and [N’Golo] Kante into babies - take him out now.”
While a third held nothing back, with “There is no future at Chelsea with Lampard as head coach - no game plan, no tactics.”
And a fourth added: “Lampard can get the f*** out now please.”
A fifth laid into the manager’s transfer strategy, with: “When you spend £220million to improve a squad, every talent you buy needs to be starting line-up material.
“I want Lampard out by Monday close of business.”
With a sixth suggesting who should be his replacement, with: “I wonder what Thomas Tuchel is doing right now.”
And a final supporter simply said: “Lampard, I love you but goodbye.”
Ilkay Gundogan opened the scoring for Pep Guardiola’s team after 18 minutes, finishing off a slick team move to curl past Edouard Mendy.
The second goal came just three minutes later when Phil Foden whipped Kevin de Bruyne’s cross past the goalkeeper at the near post.
And the third goal started at the other end of the pitch, with Raheem Sterling counter-attacking before finding the Belgian in the penalty box.
While City did not add to their tally in the second half at Stamford Bridge, they dominated play by making 17 shots on goal and six on target.
Lampard's side had some moments during the game - and did manage to clinch a stoppage-time consolation goal through substitute Callum Hudson-Odoi's strike.
It comes as Sky Sports pundit Graeme Souness laid into Lampard’s attackers for their performance against City.