Theresa May was forced into a major compromise yesterday when she had to agree to give parliament a greater role in Brexit negotiations to avert a defeat at the hands of rebels from her own party who want to keep close European Union ties after Britain leaves.
But after meeting Mrs May he told this paper: "I've been to see the prime minister and received important undertakings and made a decision to vote to give the prime minister the authority and freedom to negotiate the best deal she can".
Remain-supporting Dr Lee quit as justice minister live on stage during a speech in London, saying he could not support "how our country's exit from the European Union looks set to be delivered".
Hours before the debate began, a justice minister resigned in protest at what he called its "wish to limit" the role of parliament in shaping Brexit.
The motion to reject the Lords amendment, which would have given MPs control over the government's negotiation strategy and the final exit deal, therefore passed by 324 votes to 298 - a majority of 26 votes.
A series of further votes will take place on Wednesday, with no defeats expected after ministers agreed compromise wording over post-Brexit plans for a "customs arrangement".
In such an event, he said Parliament should be able to flex its muscles by requiring ministers to come forward with a plan of action, which MPs would be able to debate and vote on.
Liberal Democrat Brexit spokesman Tom Brake said: "As has become a tradition in Brexit negotiations, the Tories have been forced to cobble together a compromise".
Solicitor General Robert Buckland intervened four times during a speech by the former Attorney General Dominic Grieve, whose amendment would effectively give MPs a veto on the government's negotiating agenda if a deal isn't done by the end of November.
Brexit Secretary David Davis has warned Conservative Party rebels that proposals to give Parliament the power to direct negotiations with the European Union are simply a tactic to overturn the results of the 2016 referendum that mandated Britain's departure from the bloc.
Passions ran high in Tuesday's three-hour debate, when angry eurosceptics accused their rivals of trying to undermine the 2016 referendum vote to leave the EU.
Pro-EU demonstrators hold placards and wave flags as they protest against Brexit, outside of the Houses of Parliament in central London on June 11, 2018. "But if we face the prospect of a "meaningless process" rather than a "meaningful vote", Parliament will be enraged".
Theresa May saw off a revolt from the pro-European wing of her fractured party, averting what could have been a major political crisis.
The EU published an explainer of its own backstop proposal in a bid to convince the United Kingdom government of its merits, but Theresa May has said it is not acceptable because it creates a regulatory border between Northern Ireland and the UK.
Matthew Pennycook, one of the opposition Labour Party's Brexit policy team, urged lawmakers to vote to hand parliament more powers.