When someone told a lie—whether it was committed remorsefully or not, it is commonsensical to expect him/her to clear the truth.
Living in the agony of covering up a fact is hellish enough. As much as you want to reveal the truth, the ramifications may extend far beyond saving that continuing with the lie was a better choice at that point of time, as long as the truth remained unknown.
We are quick to judge liars, but if we were in their shoes, we would realize that we could have taken the same safer choice as much as we didn't like to lie.