SNP MSP Clare Adamson had expected to hold a member's debate on the case for universal benefits this week, after a notice appeared in the Scottish Parliament's bulletin stating it would take place on Thursday.
But Labour complained there was not enough cross-party support to stage the debate – and rather than step in to save it, they stood back and the debate was axed.
The Nationalists said the move showed Labour had become deeply uncomfortable discussing universal benefits since Lamont launched a party review of the issue last year and called for an end to the "something for nothing" culture.
The SNP has since promoted itself as the party of universal benefits such as free bus passes and elderly care, and accused Labour of siding with the Tories on welfare cuts.
Labour has accused Alex Salmond of trying to shut down the debate on universal benefits, claiming the SNP wants to duck hard spending decisions ahead of the independence referendum in case it turns voters against them. At Thursday's First Minister's Questions, Lamont made the charge again that Salmond was attempting to stifle the debate.
Adamson's plan for a debate was inspired by a report published in December by the left-leaning Jimmy Reid Foundation called The Case For Universalism, which argued the poor would suffer most if universal benefits were rolled back.
Her motion had the support of MSPs from the SNP and Holyrood's Independent group, but also needed at least one MSP from Labour, the Tories or LibDems to back it for a full debate.
Jimmy Reid Foundation convener Bob Thomson, a Labour member for 50 years and a former chair of the Scottish party, said the party was wrong to act as it did: "We would urge the Scottish Labour Party to see a debate on universal public services as an opportunity and not a threat.
"These are the principles on which the Labour movement was founded and many people in that movement in Scotland today want to hear Johann Lamont flesh out Labour's thinking a bit more than the slightly unfortunate soundbites which have been reported so far.
"It's no good calling for a debate if you don't take the opportunity to have a debate when it arises."
Adamson said she was "absolutely exasperated" at Labour's action and accused the party of running scared of defending its own policy.
She said: "Ever since she launched her Cuts Commission, Johann Lamont has repeatedly said she wants to have an honest debate on the affordability of universal services – yet Labour has cynically ensured that very debate won't happen in the Parliament this week.
A Scottish Labour spokesperson said: "We look forward to debating Scotland's spending priorities with the Government at every opportunity. Clare Adamson either fails to understand the parliamentary process for members' business or is being wilfully disingenuous."
The Scottish Parliament said Adamson's motion would be eligible for debate if it attracted the support of another party, but confirmed it had now been replaced by another subject raised by the SNP.
By Scottish Political Editor Tom Gordon