This change sought to give greater powers to the "sifting committee", which would be established to decide whether recommendations proposed by ministers to amend retained European Union law after Brexit would require a Commons vote.
Lee, who voted for Britain to remain in the E.U.in the 2016 referendum, said in a statement he was "incredibly sad" to resign but did so in order to vote against the government's position on a key amendment to the bill.
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.
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.
Justine Greening, a former education secretary, said she would back the rebel amendment, telling the Commons it was "sensible to have a structured process" to deal with the different scenarios that MPs could face.
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.
Her concession to discuss the changes may mean lawmakers could have more power if she fails to secure a Brexit deal, possibly leading to a softer approach to Britain's divorce.
It paid off. "I'm quite satisfied that we are going to get a meaningful vote on both "deal" and "no deal", Grieve told Sky News.
Theresa May argued that the Conservative party had to stay united to strengthen her negotiating position in Brussels.
LONDON - A junior member of Prime Minister Theresa May's government resigned Tuesday over Brexit, emboldening pro-EU lawmakers ahead of key votes in Parliament on Britain's departure from the European Union.
Tory rebels claimed that the government had agreed to specific proposals from leading backbench remainer Grieve to address concerns over what would happen if parliament rejected the final Brexit deal, or talks with the European Union were to break down.
Philip Lee said a choice between "bad and worse" options was not giving MPs a meaningful vote.
MPs will on Wednesday debate a series of other amendments to the bill, which if passed, would seek to force May to change course and negotiate to stay inside a customs union and the single market after Brexit. The Daily Express thundered: "Ignore the will of the people at your peril".
Brexit protesters outside Parliament House.