But the government does not have a majority in the Lords, and the "peers" who sit in the chamber are not elected and therefore not accountable to constituents in the way members of parliament (MPs) are in the Commons.
The legislation is not expected to be blocked by lords, but the government could be forced into making concessions as it does not have a majority in the upper house.
MPs rejected calls for the status of European Union citizens living in the United Kingdom and a parliamentary vote on the final terms of exit to be explicitly guaranteed in the bill - although ministers have conceded the Commons will have its say and it fully expects citizens of other European Union countries to be able to stay in the United Kingdom after Brexit pending negotiations.
Liberal Democrat leader, Lord Newby, pointed out the upper chamber had the power to ask the Commons to think again on any piece of legislation and hoped the Government would accept this.
MPs failed to amend the bill during its House of Commons stages despite minor rebellions by some Remain-supporting Conservative MPs.
Indeed, former speaker of the House of Lords, Janet Royall said she has "never known the PM to be present" and the House of Lords Twitter account confirmed that it was a first.
Two days of debate are scheduled for Monday and Tuesday, with the opportunity to table amendments starting on February 27.
An alliance of opposition parties, as well as some Tory peers, are expected to come together to force changes to the bill.
The House of Lords has been warned not to turn its Brexit Bill debate into a "slanging match" that pits "the peers against the people".
She added: "This Bill is not the place to try and shape the terms of our exit, restrict the Government's hand before it enters into complex negotiations or attempt to re-run the referendum". The Lords can send an amended bill back to the Commons and delay its passage, but cannot push through changes themselves.
Opening the debate, Lady Evans said she was "confident" that peers would take a "constructive approach".
"So he needs to move on, and the Labour Party need to move on, because we are now in a new reality".
"The anger of those who wanted to leave is now matched by the growing anger of those who wish to remain - particularly young people".
The shadow spokesperson for Brexit also said the House of Lords is not happy about how short the Brexit bill is and they want the "government to spell out what they're trying to achieve".
He said: "When a deal is reached the country is entitled, either directly or through Parliament, to pass judgement on what's on offer".
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