The front-runner in the race has also been pressed to keep open a sleaze investigation into Mr Johnson’s conduct.
Ms Truss, who is currently foreign secretary, has hinted she would like to stop the probe by the UK privileges committee into whether Mr Johnson misled the Westminster parliament.
She raised eyebrows on Tuesday evening after saying she would “in principle” vote to cancel the investigation. She and Rishi Sunak are yet to say whether they would keep Mr Johnson in frontline politics, or give him a peerage or knighthood.
In a letter to Ms Truss, Liberal Democrat politician Christine Jardine urged her to rule out coming to Mr Johnson’s rescue.
She said it was vital that the next prime minister “commits to restoring standards in public life” by ruling out peerages or knighthoods for Mr Johnson, among other pledges.
It is normal for former prime ministers to receive a knighthood while they remain backbenchers and then to receive a peerage on leaving the House of Commons.
Ms Jardine also said Ms Truss should put on record that she would resign if she lied to parliament.
She also said her party is looking for the ministerial code to be written into UK law, with a new independent adviser appointed to oversee it.
“During his three years as prime minister, Boris Johnson has comprehensively trashed standards in public life,” the letter says.
“From the highly concerning decisions regarding the appointment of Chris Pincher to the PM’s lies over Partygate; from the Owen Paterson affair to the Downing Street flat renovation, we have seen scandal after scandal engulf the government.
“This has all done enormous damage to public trust in politics.
“For the good of our democracy, it is essential that we seize the moment of the PM’s departure to restore that trust and make politics work for the British people once again.”
Ms Truss and her campaign chiefs have yet to respond to the letter. When Mr Johnson was forced from office last month, Ms Truss was notable among Tory ministers in saying she backed his leadership.
He has yet to say whether he will seek a new government role, or even stay as an MP – but his political career could be given an indefinite extension if a Truss cabinet gives him a life seat in the House of Lords.
He has reportedly told aides he could make a comeback, and even become prime minister again – in an apparent attempt to emulate Winston Churchill.
“The public has lost all trust in Conservative politicians. In scandal after scandal they have proven themselves to be the party of lies, of law-breaking and corruption,” Ms Jardine said.
“Both Truss and Sunak propped Boris Johnson up for months, and Truss’s comments are just the latest attempt to bend the rules and let Johnson get away with his disgraceful behaviour.
“He is clearly unfit to hold public office, let alone receive any kind of honour or peerage.”
Yesterday, Ms Truss dismissed calls to get together with Mr Johnson and Mr Sunak to discuss the cost-of-living crisis and agree on a support package before the Tory leadership contest concludes.
Describing such a meeting as “constitutionally, deeply undesirable”, the front-runner to replace Mr Johnson said she is instead concentrating on her work as foreign secretary.
“We have a chancellor, we have a prime minister. They are capable people, capable of making these decisions. This kangaroo committee you’re proposing sounds bizarre,” she said.
Mr Sunak, however, said he would be happy to get in a room with his rival and the outgoing prime minister to talk about future support for the British electorate, amid warnings about the cost of energy bills.