The ex-adviser said he was “in the room” when the PM was told intelligence officials had “serious reservations” about giving the honour to the Russian-born businessman.
It follows reports the security services changed their advice after Mr Johnson intervened.
The PM has previously denied this.
Lord Lebedev, who owns the Evening Standard newspaper, has denied posing a “security risk” to the UK.
Last week, the Sunday Times reported that in March 2020, the House of Lords Appointments Commission – which vets peerage appointments – advised Mr Johnson against granting Mr Lebedev a seat in the House of Lords on security grounds.
The newspaper said the assessment was withdrawn after Mr Johnson – a long-time friend of Lord Lebedev – personally intervened.
Another source has confirmed to the BBC that concerns were raised by security services.
Earlier, Labour deputy leader Angela Rayner asked for guarantees that Mr Johnson had never asked anyone to urge the security services to “revise, reconsider or withdraw” their advice.
Standing in for Mr Johnson at PMQs whilst he visits Saudi Arabia, Deputy Prime Minister Dominic Raab said the “suggestion” she was making was “sheer nonsense”.
But, shortly after the exchange, Mr Cummings said it was false to call the claim nonsense, and Mr Raab had been “given duff lines for the Commons by No 10”.
On his personal blog, the PM’s former senior adviser wrote: “I was in the room when the PM was told by Cabinet Office officials that the intelligence services and other parts of the deep state had, let’s say serious reservations, about the PM’s plan”.
“I supported these concerns and said to the PM in his study explicitly that he should not go ahead,” he added.
Mr Cummings says Mr Johnson reacted by becoming “very cross”, and said: “This is just … You’re just … ANTI-RUSSIAN”.
Asked to respond to Mr Cummings’s comments, a government spokesperson said: “All individuals nominated for a peerage are done so in recognition of their contribution to society and all peerages are vetted by the House of Lords Appointments Commission.”
Lord Lebedev, who also owns the Independent newspaper, was given a peerage in July 2020, for philanthropy and services to the media, after being nominated by Mr Johnson.
Writing in the Evening Standard last week, he denied posing a “security risk” to the UK, saying: “I am not some agent of Russia” and that he was “proud to be a British citizen and consider Britain my home”.
The son of billionaire Russian banker and former KGB officer Alexander Lebedev, he moved to the UK as a child, and has condemned President’s Putin’s actions in Ukraine in his newspaper, writing: “I plead with you to stop Russians killing their Ukrainian brothers and sisters.”
Ms Rayner, who was standing in for Labour leader Sir Keir Starmer, pointed to newspaper reports that claimed British intelligence warned against granting a peerage to Lord Lebedev on 17 March 2020.