The former Scottish Conservative leader said the office of Prime Minister had been “translated” by Mr Johnson.
She made the comments while out on the campaign trail with Scottish Conservative leader Douglas Ross, who argues Mr Johnson should not be removed because of the war in Ukraine.
Lady Davidson, who now sits in the House of Lords, defended Mr Ross but said she did not agree with him.
Speaking to journalists in Davidson’s Mains Park, Edinburgh, she said: “For me, to have a Prime Minister who has broken the law, laws that he set, to have presided over a culture in Number 10 where laws were repeatedly broken, and who told both the parliament and the public that no laws were broken when they were, for me that is a resignation offence.”
She said Mr Ross had been put in “a terrible position, probably the hardest position that any Scottish leader ever has been”, adding: “And as somebody who was the leader for eight years, I know what it’s like to have been dumped in it by colleagues down south.”
Lady Davidson said: “I think Douglas was pretty gutsy to come out early, to say that this wasn’t on.
“I think that his leadership of the Scottish Conservatives is without doubt, and certainly electorally, the most successful we’ve ever had – you only need to look at his results in May last year, to find 100,000 more voters across the country than I could ever find is a real achievement.
“But he, like lots of the country, take a worldview wherein there is an international conflict happening right now on Europe’s doorstep, and that now is not the time to change prime ministers.
“And I respect that view. It’s not a view that I hold.
“For me, when you’ve got a conflict where it is about supporting a country that is fighting for democracy and freedom, you have to uphold some of the rules of democracy.
“And some of the rules of democracy are that the Prime Minister leads by example, and that he or she follows the rules that they set.”
Lady Davidson said that as “a Conservative who believes deeply in the institutions of this country, it’s about having the office of Prime Minister being translated in this way, being held by somebody who has broken the laws that they themselves set”.
However, asked if the Tories will be punished by voters in the upcoming local elections, she said: “I don’t know. I think that’s for individual voters.”
The Tory peer said everyone voting in the election will already have an opinion on partygate, and the ends may not change that.
She added: “I think that there is significant evidence that the Scottish Conservatives repeatedly outperform polls at elections, and I believe we will do so again.”
Asked what offended her most about the Prime Minister’s actions, an emotional Lady Davidson said: “The thing that really gets me is how many people I know or have met or who have spoken to me or who I represented when I was still an MSP when Covid was going on, who didn’t see loved ones.
“Who stuck by the rules. Who saw people that they loved die or be ill or be alone, and who will never forgive themselves.
“And they feel that the Prime Minister and the culture in Number 10 makes a mockery of their sacrifice.”