It's more like a move in game based on the goal of best net gain. If Flynn lied it was a white lie and stuff the FBI shouldn't have known or had their noses in. He actually did the best thing in that sense in forcing them to reveal their ill gotten hand.

Punishment for changing plea is unheard of in my books when the conditions change. If you're innocent but either the cost of pleading guilty is less than proving innocence or you believe a guilty verdict is inevitable then you plead guilty to reduce the harm inflicted by a wrong verdict.

Given exculpatory evidence was suppressed putting Flynn even more in the position of being at the mercy of the prosecution then go figure.