"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", Lee, who voted to remain in the European Union during Britain's 2016 referendum, said on his website.
The opposition Labour Party wants to force the government to negotiate a Brexit deal where the United Kingdom retains "full access" to the EU's single market and that would ensure "no new impediments" to trade.
At times ministers engaged in public negotiations from the despatch box, with leading Conservative rebel Dominic Grieve and other rebels later leaving the chamber with the whips to discuss the concessions.
Commenting after Tuesday's votes, Dr Lee said: "Delighted that the government has agreed to introduce an amendment to the EU Withdrawal Bill which will give Parliament the voice I always wanted it to have in the Brexit process".
Ministers have conceded in principle to Tory rebels" demands for a "meaningful vote' on the eventual Brexit deal. "A meaningful vote is not the ability to reverse the decision of the referendum".
But in a last-ditch concession by the Government to swerve a revolt, the PM is indicating that it will put forward two of the three parts of Mr Grieve's amendment when the bill returns to the House of Lords. But a government official said they had just agreed to open talks on the basis of the rebel amendment.
"It enables parliament to dictate to the government their course of action in global negotiations".
They've been battling against Brexit on a number of fronts, including trying to ensure that Scotland doesn't lose powers back to Westminster when they come back from Brussels.
The concession means MPs could be given power to prevent Britain leaving the European Union without a deal. But there is going to be no binary choice of the deal on the table or no deal, with Parliament bypassed.
Opposition Labour lawmaker Chuka Umunna had earlier accused Britain's tabloids of intimidation, holding up Tuesday's edition of the eurosceptic Daily Express.
Another flashpoint could come when lawmakers vote Wednesday on an amendment seeking to keep Britain in a customs union with the EU.
It featured a British flag and the headline: "Ignore the will of the people at your peril".
Anna Soubry, a pro-EU Conservative MP, said she knew of one legislator who would not vote with their conscience because of "threats to their personal safety" and that of staff and family.
"The people want us to leave the EU".