The heated exchange began after the Good Morning Britain host retweeted a video posted on Twitter which appeared to show Mr Lammy with his eyes closed during the Commons debate.
“Is this why you need more time for the Brexit debate @DavidLammy?” Morgan said.
But Mr Lammy hit back soon afterwards by sharing a photograph from the same moment in the debate which shows the Labour MP checking his phone.
“More fake news, Piers,” Mr Lammy replied.
“The video has been deliberately cropped. I don’t sleep holding a mobile phone. I was replying to emails.”
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Mr Lammy was then criticised by commenters for being on his phone during the debate despite tweeting yesterday to criticise Prime Minister Boris Johnson for “giving MPs so little time to scrutinize” his deal.
The incident came just hours before Mr Johnson’s hopes of Britain leaving the EU by the October 31 deadline were dealt a blow after he suffered another defeat in the Commons.
More fake news, Piers. The video has been deliberately cropped. I don’t sleep holding a mobile phone. I was replying to emails. pic.twitter.com/hcvLIoDG17— David Lammy (@DavidLammy) October 22, 2019
MPs threw out his plan to ram legislation through the Commons approving his deal with the EU in just three days by 322 votes to 308.
The result leaves the Prime Minister effectively at the mercy of EU leaders who will decide whether to grant Britain a further extension, and for how long, in order to allow it to leave with a deal.
European Council president Donald Tusk said he would recommend they agree a further delay in order to avoid a no-deal Brexit.
Following the vote, Mr Johnson said he would “pause” the legislation while he consulted with EU leaders on what should happen next.