The Prime Minister seems to have averted disaster for her government this week - but maybe only this week.
Solicitor General Robert Buckland said the government would remain open-minded, but the meeting may not result in new proposals in the coming days.
Prime Minister Theresa May defeated the final challenges to her Brexit blueprint in parliament on Wednesday, leaving plans for Britain's departure from the European Union still largely on track but her authority weakened.
It was indicated to us that the first two parts of the Grieve amendment presented very few problems and could be incorporated into a government amendment.
"I have agreed this morning with the Brexit Secretary that we will bring forward an amendment in the Lords".
The Scottish Parliament has refused to approve the Brexit Bill, which it says would see London take back powers - albeit temporarily - from Brussels after Brexit that should by rights go to Edinburgh.
Mr Grieve said no government would survive if it tried to dispense with Parliament's input.
Those votes also show that Parliament is aware of the government's weakness and wishes to take control of the negotiations with the European Union and possibly take a softer line on Brexit than the one May's government is now pursuing.
Downing Street has officially ruled out backing Grieve's 11th-hour amendment, tabled on Monday night, making it unlikely to be put to a vote unless No 10 reverses its decision. The third part was more hard, but from the conversation there was a way forward. But Britain's second, unelected, lawmaking chamber attached various amendments, including one of a "meaningful parliamentary vote" on the deal. Known as ping-pong, the bill will move between the commons and the lords until both sides are in agreement on the text - or until the government has made enough concessions for the lords to back down.
Remainer Stephen Hammond said a group of potential rebels - believed to number 15 to 20 - received assurances from the PM moments before the key vote. He added "I absolutely trust what the Prime Minister says to us".
Brexit minister David Davis told parliament if it rejected the government's compromise on the "meaningful vote" and backed the House of Lords amendment: "What it actually amounts to is an unconstitutional shift which risks undermining our negotiation with the European Union".
But the resignation by Phillip Lee, who has always been critical of the government's Brexit strategy, underlined the deep rifts in the party over Brexit that makes such votes anything but easy.
"The Brexit secretary [David Davis] 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 global treaties, and respecting the referendum result".
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.
"She said that anything which undermines the government at home would make the negotiations with the European Union more hard".