They want Parliament to be given more powers if no deal is agreed, or if the agreement May makes with Brussels is deemed unacceptable by MPs. The decision of the Lords represents another blow for May and the appeal will have to be discussed again on Wednesday in the House of Commons.
Peers backed an amendment to the EU Withdrawal Bill by 354 to 235, a majority of 119.
Mrs May insisted she was a woman of her word and had listened to rebels' concerns and acted on them.
After an ill-judged election a year ago, May relies on the help of a deal with a small Northern Irish party to win votes in the Commons and can afford to lose no more than a handful of Conservative rebels if she is to avoid an embarrassing defeat.
Brexit supporters backing the government say if May's hands are tied by the British parliament, it is more likely to encourage Brussels to offer Britain a poor deal.
Pakistan Taliban chief killed in USA drone strike
The Afghan Taliban announced their cease-fire after Ghani unilaterally declared a temporary cease-fire for the holidays on June 7. Fazlullah and two other insurgents were killed early on Thursday morning, defence ministry spokesman Mohammad Radmanish said.
"We are absolutely confident that we will deliver a Brexit deal that. would be good for the United Kingdom, good for our European friends and partners".
The leader of the pro-EU Tory rebels has denied the Government will fall if it suffers a defeat in the Commons on its flagship Brexit bill.
The minister leading those negotiations, Solicitor General Robert Buckland, said the ruling minority Conservative government was standing by its own proposal, rejected by party rebels last week.
Her compromise failed, and on Wednesday she will again try to head off a rebellion over the so-called meaningful vote on any Brexit deal that some lawmakers want to be able to make sure the government can not accept a "no deal" with Brussels.
At last two other Tory backbenchers, former justice minister Phillip Lee and Heidi Allen, have publicly pledged their support to Mr Grieve. "But if we have no deal at all we are on the middle of frankly an extraordinary crisis".
Mexico shakes with excitement over Germany World Cup win
Germany were the clear favourites as they took on Mexico in their opening match of the 2018 FIFA World Cup . It's worth adding that defending a World Cup title is also a lot harder than pursuing one.
"I want to ensure that parliament does have a meaningful vote and I don't want to see that left to chance", said Lord Hailsham, the member of May's Conservative Party who proposed the motion. "This is the end stage of the detailed consideration of a piece of legislation", he told the BBC Radio 4 Today programme.
Expected Lords amendments to the Brexit legislation are set to return to the Commons on Wednesday.
However, the motion will be unamendable, which means MPs won't be able to insert a requirement for Mrs May to renegotiate her Brexit deal, extend the transition phase or revoke our withdrawal under Article 50.
"The meaningful vote is nothing to do with holding the government to account", Jacob Rees-Mogg, who leads a grouping of Anti-EU Conservative lawmakers, said after a speech in central London.
Blatter backs England for next European SWC
He was banned from all footballing activities for making a dishonest payment to ex-UEFA boss Michel Platini. Former Fifa spokesman Thomas Renggli told AFP that Blatter would meet Putin on Wednesday.
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