Place watermelon cubes in blender. Cover and blend until smooth. Pour watermelon puree into a pitcher. Chill or freeze until very cold.
For two martinis, in the blender combine 1 cup of the watermelon puree, 1/4 cup of the lemon vodka, 2 tablespoons of the lime juice, 1 tablespoon of the orange-flavor liqueur, and 1 tablespoon of the sugar. Add three to six ice cubes. Cover and blend until slushy. Repeat two more times.