They reassured anti-Brexit MPs that the government would accept some of their core demands to give parliament a meaningful say on the terms of Britain's European Union divorce, including - potentially - a new deadline for a deal to be agreed with Brussels that could make it hard for the government.
Lee, who voted for Britain to remain in the E.U.in the 2016 referendum, said in a statement he was "incredibly sad" to resign but did so in order to vote against the government's position on a key amendment to the bill.
Lee's resignation came as May's fragile minority government scrambled to shore up support among lawmakers before two days of debate and votes in the House of Commons on its flagship Brexit bill.
MPs will hold further votes on the EU Withdrawal Bill on Wednesday, including a House of Lords demand for the United Kingdom to remain in the EU's single market.
The government was putting a combative spin on the concessions Tuesday evening: "The Brexit Secretary has set out three tests that any new amendment has to meet - not undermining the negotiations, not changing the constitutional role of Parliament and Government in negotiating worldwide treaties, and respecting the referendum result", a spokesperson for the Brexit department said in a statement.
"We are asking members of parliament to abide by the referendum result, our manifesto commitment and to back our country", Andrew Bridgen, Conservative lawmaker and Brexit campaigner, told Reuters.
"The government can not demonstrate the flexibility necessary for a successful deal if its hands are tied midway through that process", Davis said.
The government would have to give MPs a vote on the next steps, if parliament rejects the Brexit deal - or if no deal has been reached by the end of November. "Now we have a real vote and an opportunity for Parliament to influence and approve the final deal", Nicky Morgan, a high-profile pro-EU lawmaker, said in an interview.
The change reduces the likelihood that Britain could leave the European Union without a deal if it does not like the divorce terms.
May's fragile government will be trying to defeat a rebellion by pro-EU lawmakers and reverse changes to its key piece of Brexit legislation as the matter comes before the House of Commons.
At stake is her Brexit strategy and her ability to hold her party together as she fights to deliver a Brexit divorce deal in the next 10 months.
But Tory MP Andrew Bridgen, a leading Brexit backer, said the concessions could "come back to haunt" the government if they amounted to a veto over the terms of the UK's departure.
Rebels have said they will challenge May's plans to leave the customs union during votes on other bills, on trade and customs, which will be brought back to the house some time before July 24.
Two years after Britain voted to leave the European Union, and eight months before it's due to leave on March 29, 2019, the bloc is frustrated with what it sees as a lack of firm proposals from the United Kingdom about future relations.
Either way, the chances are increasing that Parliament will get a greater say over Brexit.
A paper laying out the UK government position, due to be published this month, has been delayed because the Cabinet can not agree on a united stance.
Commenting after Tuesday's votes, Dr Lee said: "Delighted that the government has agreed to introduce an amendment to the EU Withdrawal Bill which will give Parliament the voice I always wanted it to have in the Brexit process". The Daily Express featured the British flag as its front page with the headline: "Ignore the will of the people at your peril".
The debate, which lasted for almost three hours, was split down the usual non-partisan lines that have emerged as a result of Brexit, with the likes of Labour's Kate Hoey and John Mann saying they would back the Conservative government, while Tories including Ken Clarke and Anna Soubry spoke in favour of Grieve. "It is clear we don't just want to have a chat but a proper discussion and negotiation".