I don't understand what that means. The oath of a witness is an affirmation that statements made about what the witness experienced will be truthful, but it seems to me that a promise to do something in the future would require a completely different sort of oath, and not keeping that promise wouldn't qualify as lying to Congress. Is there a law against breaking a promise to Congress?

"After careful consideration, I have concluded that Brett Kavanaugh and I have no choice but to resign for our inexcusable transgressions during our school days. I will leave it to Justice Kavanaugh to finalize our joint resignation."