Lee's resignation Tuesday comes ahead of a crucial 48 hours for the government as it battles to hold off a series of potential rebellions to remove 15 amendments laid by peers in the House of Lords created to strengthen parliament's hand in the negotiations.
"I am trying to negotiate the best deal for Britain", she told MPs.
The resignation comes as the Commons prepare to take part in crunch votes on the Brexit bill.
A UK Conservative MP has resigned as justice minister in protest at Prime Minister Theresa May's Brexit policy.
May, who faces one of her most crucial weeks since becoming prime minister, will address the backbench Conservative 1922 Committee on Monday evening to tell her MPs that, even though the EU Withdrawal Bill is a largely technical matter, the way they vote will send out a highly important signal to the country.
It follows an article in the Sunday Telegraph co-authored by two senior Conservatives, Remainer Amber Rudd and Brexiteer Iain Duncan Smith, calling for unity in the party, and warning that any rebellion will only play into the Labour leader's hands. 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.
Lee, who was Parliamentary Under-Secretary of State at the Ministry of Justice, has quit the front bench so he can vote against the government on the "meaningful vote" amendment. On Wednesday, it will debate an amendment instructing the government to negotiate a customs union with the EU.
Other amendments from the Lords to be debated Tuesday include transferring the EU's Charter of Fundamental Rights into United Kingdom law and one forcing the government to negotiate to remain in the European Economic Area (EEA) like Norway.
The minister said the "badly rushed" Brexit legislation, and his belief that MPs needed to have a meaningful vote on the final deal agreed with Brussels, gave him no choice but to walk away from his post at the Home Office.
"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", he said. MPs will vote on this particular amendment this afternoon.