During an impassioned speech she pleaded for the government not to go "over the cliff" into a hard Brexit and warned MPs not to ignore the 48% of the United Kingdom who voted to remain.
Pro-EU Conservative backbenchers had threatened to defy the prime minister and vote in favour of giving parliament a "meaningful vote" on the Brexit deal.
Dr Lee said his main objection to Government policy was over the "wish to limit Parliament's role in contributing to the final outcome" and signalled he would rebel on the issue in the Commons later.
The government would not have sought a deal if it thought it had the votes to win, and they clearly blinked.
"They had every opportunity to question Theresa May, they come not to and the message is quite clear: a unified Conservative Party, working together will deliver the Brexit that the people voted for".More news: White House Seeks to Block Senate Bid to Kill ZTE Deal
However, leading Brexiteer Tory MPs and ministers have suggested May had only agreed to further discussions on supporting Tory rebel Dominic Grieve's amendment.
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 for now, the government seems to have prevented an embarrassing defeat, and the Tory rebels have avoided the unpleasantness of colluding in the defeat of their Prime Minister.
She added: "Everybody now has to stand up and be true to what they believe in".
But, the pro-EU MPs' version of what they were promised appears to differ from what they government says it offered, threatening to reignite the dispute and reviving the possibility of a revolt that would badly damage May's authority. But there is going to be no binary choice of the deal on the table or no deal, with Parliament bypassed.
But Mr Grieve's amendment demands that if there is no agreement with Brussels before the end of November MPs would vote on a motion setting out what should happen next.More news: Geraint Thomas wins the Criterium du Dauphine ahead of Adam Yates
"If she has given too much away I think there will be real anger towards her".
The key Brexit bill is back in the Commons today and tomorrow for a series of knife-edge votes that will determine the future of the Brexit process.
Remainers see it as a road map to ensuring Britain leaves with a good deal.
British Prime Minister Theresa May faces another day of Brexit compromise at Westminster.
There are mutterings from Brexiteers that a betrayal on this could be the moment they go over the top and withdraw their support from the prime minister; this is a showdown averted but not killed off.More news: Mother issues warning after MS girl diagnosed with ‘tick paralysis’
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