Parliament will vote on another series of so called "Brexit wrecking" amendments later on Tuesday, some of which seek to commit the government to remaining a member of the EU single market and "a customs union", while another aims to steer the United Kingdom toward membership of the European Economic Area.
Conservative former minister Anna Soubry said the abuse of MPs who speak out against the government's Brexit policy "simply has to stop".
Lee said "the people, economy and culture of my constituency will be affected negatively" by Britain's European Union departure, and it is "irresponsible to proceed as we are".
The Lords Brexit Bill amendment had called for the government to make it a negotiating objective to remaining in the EEA.
The European Union Withdrawal Bill, meant to enact Britain's exit from the bloc, has had a rocky ride through Parliament.
The House of Lords defeated the government 15 times in earlier votes, offering parliament the chance to put pressure on May and her government to change tack on Brexit.
But it was a vote in parliament on Tuesday that left her seemingly at the mercy of two groups in the Conservative Party - those who want to maintain the closest possible ties with the European Union, and others pressing for a clean break.
Brexit protesters outside Parliament House.
Further votes on EU Withdrawal Bill amendments will take place on Wednesday, with no defeats expected for the government after ministers agreed a compromise wording over post-Brexit plans for a "customs arrangement".
Earlier in the day during the debate on the "meaningful vote" clause of the EU Withdrawal Bill, Tory rebels were threatening to impose a government defeat until May's intervention.
"We must under all circumstances respect the result of the referendum", Brexit Secretary David Davis told lawmakers as he opened the debate.
There was little doubt the government would win on the customs union and single market, which some pro-EU lawmakers say is the only way for Britain to retain economically advantageous close ties with the bloc, with the opposition Labour Party also divided over future relations.
"It's not practical, it's not desirable and it's not appropriate", he said. The Daily Express thundered: "Ignore the will of the people at your peril".
A file photograph of justice minister Phillip Lees.
She told the Commons: "The central choice for Parliament is whenever we accept the outcome of the referendum or do we seek to subvert that process?"
The pro-independence party accuses the British government of trying to seize powers that will be handed back from Brussels after Brexit and which the SNP believes should go to Scotland's Edinburgh-based parliament. May's preferred approach is temporarily keeping the U.K.in some form of temporary customs union with the E.U., but this is unacceptable to hardline Brexiteers in her party. 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 closely aligned to the bloc, Britain's biggest trading partner.
Not at all. Among the many issues outstanding ahead of Britain's planned withdrawal date of March 29, 2019 is the question of what happens to the Northern Irish border.