1In 1-quart saucepan, heat lemon-thyme simple syrup ingredients over low heat until sugar is dissolved. Let stand 15 minutes. Strain to remove thyme and lemon peel. Use within 2 days.
2Place 1 sprig fresh thyme in cocktail shaker. Add vodka, cranberry juice, 1 oz of the lemon-thyme simple syrup and liqueur; muddle thyme with back of spoon. Add ice; place lid on shaker, and shake until cold and blended. Strain into 2 martini glasses.
3Garnish with lemon slice and sprig of thyme.