The U.K. voted to leave the political and economic bloc of 28 nations in June 2016.
"The main reason for my taking this decision now is the Brexit process and the government's wish to limit parliament's role in contributing to the final outcome in a vote that takes place today", Lee, who voted to remain in the European Union during Britain's 2016 referendum, said on his website.
But while the well-worn arguments focusing on the nature of a meaningful vote were made, the real drama was taking place on the floor of the chamber where chief whip Julian Smith, solicitor general Robert Buckland and Brexit secretary David Davis as well as the Prime Minister's parliamentary private secretary (PPS) George Holingberry were in deep discussion with each other and Grieve, as they sought to avert an embarrassment for the government.
Who is the minister who has resigned?
Prior to the votes, the government suffered its first ministerial resignation over Brexit as Phillip Lee quit the Ministry of Justice so he could speak out freely.
"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", he said.
The amendment in question hinges on whether lawmakers will get a "meaningful" vote on Britain's membership of the European Union.
May says the changes would weaken the government's negotiating position, and the government will try to alter or reverse them in the House of Commons on Tuesday and Wednesday.
So the government scraped through without a defeat - but not without paying a price.
However, a potential rebellion by pro-Remain Tories over their demands for a "meaningful vote" on the final Brexit deal was only avoided after ministers agreed at the last moment to discuss a compromise. If she fails to deliver on her promises, she will lose their goodwill and face a backlash she won't be able to contain, people familiar with the matter said. The strength of this commitment is yet to be seen in writing - and the Brexit department is still insisting it has not given up control of the negotiations - but the anti-Brexit rebels showed they have the numbers to force a defeat should the government renege on its pledge. The Labour party, the main opposition, is also divided on Brexit.
As with last week's set-to with Davis over the Northern Irish backstop, both sides of the Brexit culture war in the Tory party were nearly immediately in dispute about what the climbdown meant - and who had won.
What do the newspapers say about the votes?The Daily Express featured the British flag as its front page with the headline: "Ignore the will of the people at your peril".
If the government avoids defeat, is Brexit a done deal?An open border is one of the key guarantees of the Good Friday Agreement, which ended decades of sectarian violence in Northern Ireland.
Which side won on Tuesday will become much clearer in the next few days, when the government amendment is tabled in black and white.
May's divided cabinet has yet to settle on what sort of customs deal Britain should have with the European Union - an issue of crucial importance to businesses with cross-border supply chains, and the land border between European Union member state Ireland and the British province of Northern Ireland.
It is a politically explosive issue with no obvious solution. "But if the Lords amendments are allowed to stand, that negotiating position will be undermined".