Mr Corbyn returned to the attack during Prime Minister's Question on Wednesday.
Mr Lammy, a supporter of Best for Britain, told the Press Association that Mrs May had to confront the fact that there was no majority in Parliament for the deal she has negotiated with Brussels, or for any other proposed deal, such as Norway-style single market membership or a Canada-plus free trade agreement.
She went to Brussels at the end of a week in which she delayed the Commons vote on her Brexit deal, admitting it would be rejected by a significant margin, and then went on to survive a vote of no confidence in her leadership by Conservative MPs by 200 votes to 117. "That is what we are going to do".
The wording of the motion, targeted at May rather than the government as a whole, would not trigger the process set out under the Fixed-term Parliaments Act which could eventually lead to a General Election.
The crucial vote - which was postponed earlier this month to avoid a heavy defeat - will take place the following week.More news: US Offers USD 4.5 Bln Investment in Central America, Mexico
Housing Minister James Brokenshire told BBC Radio the government was making no-deal preparations "reluctantly".
Labour insisted it was clearly a confidence motion and should be allocated time for debate by the Government.
May's spokesman said that would be done "shortly".
Jeremy Corbyn, leader of the opposition Labour Party, accused May of deliberately wasting time, delaying the vote to force Parliament to choose between her deal and no deal.
The UK government is preparing to spend up to £2bn on Brexit measures in the coming weeks as it looks increasingly likely that Britain will crash out of the European Union without a deal on future trading arrangements.
The Prime Minister delayed a Commons vote on her deal this month while she sought further reassurances from the European Union which could make it more acceptable to hostile MPs.More news: US Hits Russian Spies With Fresh Sanctions Over Election Meddling
"It's not what we want to do, it's not what we still expect to do because we want to see the deal secured, the vote through parliament, but I think it is right and proper that we maintain our work on preparing for a no-deal", he said.
Mrs May will say: "Let us not break faith with the British people by trying to stage another referendum".
But one of Mrs May's closest allies said "all options" should remain open if the deal is rejected.
Speaking after the Cabinet agreed to step up no-deal preparation, Mr Barclay said: "Parliament needs to back the deal because the outcome of not doing so is we risk the default of no-deal and a responsible government must prepare for that eventuality".
The appearance follows Mrs May's de facto deputy, Cabinet Office Minister David Lidington, and the PM's chief of staff, Gavin Barwell, both dismissing reports that they are planning for a new referendum.
"There will be an very bad lot of fuss and noise and then people will realise that they voted to trigger Article 50, the terms of which are absolutely clear".More news: Tesla Model S catches fire-twice-after flat tire in California
Mrs May on Monday said the government was preparing for a "no-deal" Brexit and "the Cabinet will be discussing the next phase in ensuring we are ready for that scenario". A source said a copy of May's statement was sent to the opposition at 3pm, "give or take", under the terms of an existing agreement, which contained the "already-agreed decision" to hold the vote in the second week after Parliament returned from the Christmas recess.