Remain-supporting Dr Lee quit as justice minister live on stage during a speech in London, saying he could not support "how our country's exit from the European Union looks set to be delivered".
The House of Lords amended the Bill so that if MPs reject the deal, they can direct ministers to go back and renegotiate.
He called for Brexit, now set for March 2019, to be delayed and for the public to get a second referendum on the terms of any exit deal.
After the resignation of justice minister Phillip Lee, who said he could not support the government's position on Brexit, it was said government whips feared a Tory rebellion on the "meaningful vote" amendment passed by the House of Lords.
In a highly charged atmosphere in parliament, lawmakers who oppose the government said they had received death threats and brandished a copy of one of Britain's tabloid newspapers, the Daily Express, which ran a headline saying: "Ignore the will of the people at your peril". "I'm looking forward to the discussions and it's right to say that I'll be looking at potential drafts of what an amendment could say", he said.
The amendment in question hinges on whether lawmakers will get a "meaningful" vote on Britain's membership of the European Union.
"I think it is hugely irresponsible and I can't believe that those that are perpetrating this don't know exactly what they're doing".
"If Brexit is worth doing, then it is certainly worth doing well; regardless of how long that takes", he said. "It is, however, irresponsible to proceed as we are".
The Lords amendment would have given parliament the power to decide what happened next, with the possibility of going back to the negotiating table or even staying in the bloc.
She told BBC Radio 4's World At One that "at least half a dozen" junior ministers had been "very uncomfortable for some time" at the Government's direction on Brexit.
Man dies after gang attack in his home
Mr Wilk died later in hospital, while his partner remains in hospital and is undergoing treatment for her injuries. After the armed men fled the scene, a vehicle was found burned out in the Waterfall area around five miles away.
But these putative pledges by the PM are inconsistent with Tuesday night's statement by Davis's officials that any new amendment relating to the power of MPs to accept or reject a Brexit deal must not restrict her negotiating freedom - or restrict her ability to sign whatever treaty with the European Union she would like.
May is seeking to overturn 14 of 15 Lords amendments, but has a fight on her hands due to her fragile majority in the 650-seat Commons.
The government would not have sought a deal if it thought it had the votes to win, and they clearly blinked. Mr Grieve's proposal will now be added to the legislation.
Liberal Democrat Brexit spokesman Tom Brake said: "As has become a tradition in Brexit negotiations, the Tories have been forced to cobble together a compromise".
"Grieve's amendment puts that right and in a way Govt could and should accept it".
Amendment 19 would enhance the powers of parliament in the Brexit process by making a Commons vote on the final withdrawal terms a "meaningful vote".
It would also give hard Brexiteers the chance to "scupper a good deal", she claimed.
She has already agreed to give MPs a vote on the final Brexit deal, but says it will be a yes or no decision - meaning that rejecting it could see Britain crash out of the EU.
However, despite backing down, pro-Remain Tories signalled they would not be easily consoled by a compromise offered by ministers.