The adjective mendacious refers to something that is not truthful; or that it is lying or false. You can certainly fix a falsehood (or a mendacity) by telling or revealing the truth — and be willing to accept the consequences if you're the one who started the lie.
Does mendacious refer to something that is fixable (mendable)?
In Tess of the d'Urbervilles, by Thomas Hardy, John Durbeyfield is walking home. He encounters a local parson who tells him of his family history: The poverty-stricken Durbeyfields are descended from the once famous d'Urbervilles, a wealthy family dating back to the time of William the Conqueror.
Here, John questions the parson about the location of the family manor:
And where do we raise our smoke, now, parson, if I may make so bold; I mean, where do we d'Urbervilles live?"
"You don't live anywhere. You are extinct — as a county family."
"Yes — what the mendacious family chronicles call extinct in the male line — that is, gone down — gone under."
"Then where do we lie?"
"At Kingsbere-sub-Greenhill [cemetery]: rows and rows of you in your vaults, with your effigies under Purbeck-marble canopies."