WASHINGTON — When Michael D. Cohen admitted this past week to lying to Congress about a Russian business deal, he said he had testified falsely out of loyalty to President Trump. When he admitted this summer to lying on campaign finance records about payments to cover up a sex scandal during the campaign, he said it was at Mr. Trump’s direction.

Paul Manafort and Rick Gates, former senior Trump campaign officials, lied to cover up financial fraud. George Papadopoulos, a former Trump campaign aide, lied in hopes of landing an administration job. And Michael T. Flynn, another adviser, lied about his interactions with a Russian official and about other matters for reasons that remain unclear.

If the special counsel, Robert S. Mueller III, has proved anything in his 18-month-long investigation — besides how intensely Russia meddled in an American presidential election — it is that Mr. Trump surrounded himself throughout 2016 and early 2017 with people to whom lying seemed to be second nature.

They lied to federal authorities even when they had lawyers advising them, even when the risk of getting caught was high and even when the consequences for them were dire.