Dr Lee joins the back benches and says he will support an amendment to the EU Withdrawal Bill which is being debated and voted on in the House of Commons.
The concession means MPs could now be handed the power to seek to prevent Britain crashing out of the European Union without a Brexit deal.
Another flashpoint could come when lawmakers vote Wednesday on an amendment seeking to keep Britain in a customs union with the EU.
Remain-supporting Conservative MPs had threatened to defeat the government on an amendment to the bill which would have given Parliament a wide-ranging veto to May's Brexit deal, or even force a second referendum.
They are rallying around an amendment giving the House of Commons power to send the government back to the negotiating table with Brussels if lawmakers don't like the terms of the Brexit deal struck with the EU.
Five Labour MPs also rebelled by voting in favour of disagreeing with the Lords amendment: Ronnie Campbell, Frank Field, Kate Hoey, John Mann and Graham Stringer.
"It would be the end of the Conservative party if they succeed", he said.
He offered to use the proposal as the basis of discussions "in good faith" before the bill returned to the Lords, in exchange for support for the government on Tuesday.
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Asked whether such concessions would nowAsked whether such concessions would hamper Britain's negotiating hand, Mr Grieve continued: "I disagree with that entirely".
And to avoid a sudden "cliff edge" on Brexit day, 29 March 2019, it would also convert existing European Union law into United Kingdom law so the government and Parliament can decide at a later date which bits they want to keep or change.
A Conservative MP has resigned from his ministerial role ahead of a crucial Brexit vote in parliament.
In a tense afternoon in parliament, Remain MPs said they had received death threats and brandished a copy of the Daily Express newspaper, which ran a headline saying: "Ignore the will of the people at your peril".
"I am confident I can get a deal that allows us to strike our own trade deals while having a border with the European Union which is as frictionless as possible", she said. If and when agreement can be reached, the new amendment will be introduced in the House of Lords, when the bill returns there in the next stage of its passage through parliament. It also attacked the unelected nature of the House of Lords (which traditionally scrutinizes laws passed to it by the elected lower chamber), linking it to a perceived attempt to frustrate the Brexit process.
"The people want us to leave the EU".