Does divorce befall the wife who lied to her husband, claiming she had taken birth control—despite not having taken it—so that he would stop threatening her with divorce, after he had uttered the triple divorce in the event that she had taken it?

If you did not take the contraceptive as your husband tied the divorce to it, then the divorce does not take effect. You must tell him the truth and repent to Allah for lying, and advise him kindly regarding threatening divorce. Be careful not to use contraceptives without his permission in the future, as procreation is a right of both spouses.