Theresa May is facing one of the biggest tests of her leadership, with Tory rebels threatening to vote against their own party to force through amendments to the bill.
The amendment in question hinges on whether lawmakers will get a "meaningful" vote on Britain's membership of the European Union.
Dr Lee's shock departure came as Brexit Secretary David Davis warned potential Tory rebels that they can not undo the European Union referendum, ahead of a tricky 48 hours in which the Government will try to get its Brexit programme back on track.
What does his resignation mean for the government?
"That term, Mr Speaker, is actually specifically defined in the Belfast Agreement and I've no doubt that government ministers will have read the Belfast Agreement in its entirety", she said.
If May is defeated by a wide margin her position as Prime Minister could be threatened. This might convince some wavering "rebels" to back the government in order to save May and prevent Boris Johnson, the current foreign secretary and a leading so-called "Brexiteer", from seeking to replace her.
"Here we are on the eve of an important June summit. and we've no landing zone".
There were no major surprises among the Labour benches, with all those who sided with Theresa May being well-known Brexit backers.
The government concession is all the more remarkable because of the strength of opposition to the original amendment from ministers.
What do the newspapers say about the votes?
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".
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.
Under the proposal, if no deal has been reached with Brussels by this point, the government will return to the House of Commons to determine the next course of action.
Talks with Brussels have stalled over the fraught issue of the Irish border, but both sides are hoping to agree a final deal by October in time for the break on March 29, 2019.
Also on Tuesday, the government successfully overturned an attempt to remove the date of Brexit from the face of the bill.
It concludes that the UK Government's backstop would not serve its central objective of avoiding a hard border.
May's Cabinet is divided between ministers including Foreign Secretary Boris Johnson, who support a clean break with the European Union, and those such as Treasury chief Philip Hammond who want to keep close ties with the bloc, Britain's biggest trading partner.
The minister also showed a united front with the Prime Minister by denying reports he came close to resigning.
The government averted a rebellion on Tuesday over whether Parliament should have a decisive say in such a scenario.