Peers are voting on whether to give Parliament a potentially decisive say over the outcome of Brexit talks.
An amendment to the EU Withdrawal Bill tabled by Viscount Hailsham would give MPs the power to ask Theresa May to return to the negotiating table if it decided her deal was inadequate.
He said Parliament, not ministers, must “determine the future of the country”.
The PM says Parliament will have a meaningful vote but it remains unclear what happens if the deal is rejected.
The UK is due to leave the European Union on 29 March 2019.
Both sides hope to negotiate the UK’s withdrawal agreement by this October in order to give the UK and European Parliaments enough time to debate and vote on it before the moment of departure.
The government is at risk of defeat on Monday as it does not have a majority in the Lords and has already lost a number of votes on its main Brexit legislation.
The Conservative peer’s amendment would allow Parliament to determine the government’s course of action if MPs rejected the deal or if the UK and EU were not able to reach an agreement of any kind.
Ministers have indicated that the UK would leave anyway in the event of either of these scenarios.
Tory spokesman Lord Callanan said Parliament’s vote would be binding but if it did reject the deal the EU’s Article 50 process – determining the timetable for leaving – would “kick in” and the UK would still leave.
‘Duty to our country’
Last week Brexit Secretary David Davis said the motion to be considered by MPs on the final deal would be amendable – raising the prospect of MPs having greater influence over the process.
The Hailsham amendment would also give Parliament control of the process if the legislation enshrining the withdrawal treaty promised by ministers was not approved by 29 March 2019.
The peer, who as Douglas Hogg was an MP for many years, told the House of Lords the principle of parliamentary sovereignty was “fundamental to our liberties and must not be betrayed” when it came to Brexit.
“Whatever our party affiliation, our duty as parliamentarians is to our country and our conscience,” he said.
But former Conservative leader Lord Howard said the idea of effectively giving Parliament a veto over Brexit – which the public voted for in a 2016 referendum – was “fundamentally misconceived”.
“I’m afraid it reveals the appalling lengths to which the die-hard Remainers are prepared to go to achieve their aims,” he said.
The government has already been defeated on the issue of a meaningful vote in the Commons. In December, MPs voted in favour of a legal right to have their say on the withdrawal deal.