What type of lie was this? If it was calumny, then yes it would be continuously sinful not to correct the damage done to another’s reputation.
If it was not calumny but did concern something where the other person had a right to know, then you probably do not have an obligation to admit to lying, but may have an obligation to correct whatever damage you’ve caused, by other means.
If it was concerning something where the other person had no right to the truth, then there is no obligation to correct the matter unless they bring it up again.