The Lib Dems, who identify strongly as an anti-Brexit party to the point of pushing for a second referendum and running by-elections in Remain-friendly seats on that platform, opposed the Government.
May also told them she would try to capture another of their concerns, as enshrined in Grieve's amendment to the EU Withdrawal bill - which would much more explicitly give MPs the whip hand in Brexit talks, if May has still not done a deal with the EU by February next year. The victory was Pyrrhic, as the government's earlier climbdown all but ensures MPs will have an increased say on the terms of any deal.
Ms. May has said a government defeat would weaken its hand in exit talks with the European Union.
"In all conscience, I can not support the Government's decision to oppose this amendment because doing so breaches such fundamental principles of human rights and Parliamentary sovereignty".
"A vote between bad and worse is not a meaningful vote. And I can not bring myself to vote for it in the bastion of liberty, freedom and human rights that is our Parliament".
Dr Lee added: "If Brexit is worth doing, then it is certainly worth doing well; regardless of how long that takes".
"Secondly, we can not change the fundamental constitutional structure which makes the Government responsible for worldwide relations and global treaties".
The Government has won this key vote, but not without having to make some significant concessions.
'The goal of the EU Withdrawal Bill is simple - it is putting EU legislation into law to ensure a smooth and orderly transition as we leave, ' she is expected to tell them.
"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".
Yet, the Labour camp is split on the Brexit issue between pro-Leave MPs ready to vote with the government, and rebels who've come out against their own party's amendment to support the country's membership in the European Economic Area.
He confirmed that ministers will seek to overturn 14 amendments which he said would undermine the goal of the Bill and fail to respect the result of the 2016 referendum.
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.
Grieve told MPs: "If we don't achieve a deal at all, the fact is we are going to be facing an huge crisis".
Remain-supporting Conservative MPs had threatened to back an amendment to the bill which would have given parliament a more widespread veto.
May had earlier warned that defeat would weaken her hand in exit talks, while a string of eurosceptic MPs stood up to accuse the rebels of trying to thwart Brexit.
"Grieve's amendment puts that right and in a way Govt could and should accept it".
Her fellow Conservative backbencher Stephen Hammond said: "Parliament must be able to have its say in a "no deal" situation".
In a day of drama at Westminster, ministers caved into the rebel demands for a "meaningful vote" on Brexit in order to prevent a defeat on the EU Withdrawal bill which could have triggered a leadership crisis for the prime minister.