The government chief whip faces calls to resign over allegations he used underhand tactics to win crucial Brexit votes - and then tried to cover it up.
Pairing is a parliamentary convention by which pairs of MPs on different sides of the Commons agree not to vote so that an absence such as maternity leave does not count against a member.
Mr Lewis had been "paired" with Liberal Democrat deputy leader Jo Swinson, meaning neither would walk through the voting lobbies.
Ms Swinson gave birth to her son Gabriel on June 29.
But according to The Times, Mr Lewis and two other MPs were told by Mr Smith that they should vote, despite being paired.
It was reported that Mr Smith told the chief whip of another party that he had deliberately sought to break pairing arrangements, but didn't realise Mr Lewis was paired with Ms Swinson.
Earlier, Mrs May told MPs the breaking of the pair was "done in error".
Labour has called for the chief whip and party chairman to resign if they can not fully explain what happened.
"This Government is rotten to its core. Julian Smith and Brandon Lewis must now resign or be sacked, and Theresa May must apologise for misleading the House".
She said it was "absolutely abhorrent to be calling out me in particular" and, referring to the Swinson breach, added: "I assured the house yesterday that it was an error".
Conservative MPs Anna Soubry, Peter Bone and Heidi Allen also raised concerns. "Without those, what's left?"
A Conservative spokesman stopped short of denying the reports.
Asked if the PM stood by her comments that the pact had been broken in error, a spokeswoman replied: "Yes, absolutely".
But in a letter to Mark Sedwill, the acting Cabinet Secretary, Labour's shadow Cabinet Office minister Jon Trickett said the reports the agreement was broken on objective showed there was "an orchestrated attempt by the government to cover up their actions".
Andrea Leadsom, the Commons Leader, told MPs it was a "mistake".
"If they can't do so, surely the chief whip and Conservative Party chair should resign". A report by the cross-party Commons procedure committee has already set out how one could be set up, including proxy voting for parliamentarians who are absent after giving birth or through illness, but no action has been taken yet.
That prompted an angry response from Leadsom, who said that she was one of the Conservatives pairs on Tuesday night. "No other pairs offered on the trade bill on Tuesday were broken".
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