"If, in the future, I am to look my children in the eye and honestly say that I did my best for them I can not, in all good conscience, support how our country's exit from the European Union looks set to be delivered".
The speech will come on the eve of two days of debates and voting on amendments to the EU Withdrawal Bill, which is scheduled to last 12 hours.
"So Theresa May needs to win these votes and I think she will".
In a rare alliance, senior Tory Remain and Leave MPs have urged party rebels to back Prime Minister Theresa May on the bill.
The MP says he will back a knife edge vote created to give parliament the power to vote down May's Brexit deal.
Speaking to reporters outside the meeting, Solicitor General Robert Buckland confirmed the Government was in discussions with rebels about establishing a fresh amendment committing to seek a customs arrangement - not a union - with the EU.
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Brexit Minister Steve Baker said the Government would "look very carefully" at the amendment, which is being tabled by former Cabinet Ministers Oliver Letwin and Nicky Morgan.
Conservative whips have also offered MPs a 28-day "cooling off" period if the Commons rejects the final Brexit deal in a "meaningful vote" promised by the government, during which ministers would have to explain their next steps.
The Edinburgh South MP added that he was "confident we can smooth some of the particularly rough edges" of the Withdrawal Bill, and said he believed there were enough Conservative rebels to keep the United Kingdom in the customs union.
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.
Senior backbencher Jacob Rees-Mogg said he expected there would be enough unity in Conservative ranks to see the Bill through.
Mr Buckland, who was a Remain supporter, was standing alongside junior Brexit minister and Leaver Steve Baker when he made the comments.