Helga is well known to be perfectly virtuous. Her best friend Kurt is accused of conspiring to peacefully overthrow a tyrannical government, and will be tortured to death and executed unless Helga can convince government agents that he did no such thing. As a matter of fact, Helga has conclusive first-person evidence that Kurt did no such thing, much as that government deserves to be overthrown.
Suppose that it is sometimes permissible to lie. Then surely lying to save a peaceful conspirator against a tyrannical government would be a paradigm case of permissible lying, and indeed of obligatory lying. Thus, if Helga testifies to government agents that Kurt is not a conspirator, she is doing precisely what a perfectly virtuous person would do if Kurt were a conspirator. Thus if she is known to be perfectly virtuous, her testimony to Kurt's not being a conspirator is unworthy of credence. In fact, her testimony would be more worthy of credence if she were somewhat less virtuous and rigidly opposed to lying in all cases. Thus the permissibility of lying would make the testimony of the virtuous be worthless in a number of high-stakes cases.
But the virtuous are precisely the people whose testimony should carry weight, they are precisely the trustworthy, at least in cases where they are in a position to know whereof they speak. So the conclusion that Helga's truthful testimony about Kurt is worthless is paradoxical. And this paradox gives one reason to reject the premise from which the paradox was derived, namely that it is sometimes permissible to lie.