Using two wide, flat plates, pour about 2 tablespoons of lemon juice in one plate and about 3 tablespoons of granulated sugar in the other. Dip the rim of a martini glasses in the lemon juice, then roll the wet rims in granulated sugar. Set coated glasses aside.
Fill a cocktail shaker with ice and add vodka, limoncello, sweet and sour mix, lemon juice, and sugar. Shake well. TIP: A standard shot glass holds about 1.5 oz.
Pour into prepared martini glasses. Garnish with a floating slice of lemon.