Jeremy Corbyn has been urged by the Momentum founder and a long term ally of the Labour leader to sack Chris Williamson
Mr Lansman said Mr Williamson had not shown "one iota of contrition" after saying the party had been "too apologetic" in the face of criticism of the way it dealt with anti-Semitism within its ranks.
The Derby North MP - a strong supporter of Mr Corbyn - was controversially readmitted to the party on Wednesday after being issued with a formal warning by a National Executive Committee (NEC) anti-Semitism panel.
The decision produced a furious backlash, with more than 120 Labour MPs and peers led by deputy leader Tom Watson demanding Mr Corbyn step in to withdraw the Labour whip.
One of those Jess Phillips insisted that it was a "matter of principle" for the Labour Party.
She said he had been guilty of "a litany of offensive behaviour towards the Jewish community and those fighting anti-Semitism".
Ms Phillips told the BBC Radio 4 Today programme: "This is a matter of principle about racism, about the Labour Party being the party of equality, the party that is anti-racist. That reputation is slipping away from us every day.
Nearly 100 Labour staff members have written to the party's general secretary Jennie Formby urging her to launch a review of the decision to let Mr Williamson back in.
They they would be "made to feel unwelcome by his presence whilst at work" unless the decision to lift his suspension is not overturned.
They were backed by Mr Lansman - one of Mr Corbyn's oldest allies - who accused Mr Williamson of showing "contempt" for the panel's ruling after he tweeted that he had received an "avalanche" of support from grassroots members.
In response, Mr Lansman tweeted: "This tweet reveals not one iota of contrition nor any acknowledgement of wrongdoing following a further formal warning from the Labour Party for behaviour grossly detrimental to the party. Such contempt for the party's verdict! He has to go!"
A Labour source insisted that Mr Corbyn was not involved in the party's disciplinary processes or individual cases.
"It would be wholly inappropriate for a leader to pick and choose cases in the way that is being demanded," the source said.
"Several of the MPs who have signed (Mr Watson's statement) have in the past argued against political interference."
However, it emerged one of the members of the three-member panel which agreed to let Mr Williamson back into the party with a warning has called for the decision to be reviewed.
Leicester East MP Keith Vaz has written to general secretary Jennie Formby expressing concern that the leaking of its ruling on Mr Williamson to the media meant its decisions in other cases could be subject to legal challenge.
He said that to ensure the "complete integrity" of the process, either a new panel should be convened or all the cases it dealt with on Wednesday should be referred to the party's disputes committee for reconsideration.
Mr Williamson was suspended in February after video footage showed him telling a meeting of the Momentum group that Labour's reaction to anti-Semitism allegations had led to the party being "demonised".
He was also filmed saying he had celebrated the resignation of MP Joan Ryan, who quit Labour in protest over the handling of anti-Semitism and bullying complaints.
