The other sought “minutes of, submissions relevant to and electronic communications relating to” meetings between the Cabinet Office or Mr Johnson’s office and Lord Lebedev.
Labour took the unusual step of using what is known as a “humble address” procedure, meaning that its demand binds the Government if passed by the Commons.
There were reports on Tuesday morning that the Government was trying to whip Tory MPs to vote against the measure, but in the end they were asked to abstain amid signs of dissent.
The motion was eventually passed, meaning ministers must now decide how they meet the obligations in its wording.
It remains possible that ministers could choose to withhold or redact elements of what has been requested on national security grounds.
‘I have nothing to hide’
A senior government source said on Tuesday that they would consider “in due course” how to respond to the development.
Lord Lebedev welcomed the release of any advice, tweeting: “Openness and transparency are pillars of our democratic system, so I welcome the call for security advice about me provided to HOLAC to be released. I have nothing to hide.”
He also criticised Labour for triggering the debate, saying: “There’s a war in Europe. Britain is facing the highest cost of living since the 1950s. And you choose to debate me based on no facts and pure innuendo. What’s become of you Labour?”
Lord Lebedev also repeated denials about having no connections to the Russian government, tweeting at one point on Tuesday: “I have no links to the Kremlin. Never even been inside apart from the museum.”