In a large liquid measuring cup, combine lime juice and 1 ½ cups cranberry juice. Divide among 2 ice cube trays and freeze until firm, about 3 hours.
In a blender, puree flavored ice cubes, strawberries, vodka, Cointreau, and remaining 2 tablespoons cranberry juice until thick and smooth.
Divide cocktail among 4 glasses. Garnish with lime wedges.
