Combine sugar and 3 tablespoons water in a small microwave-safe bowl. Microwave at high for 2 minutes or until mixture boils, stirring every 1 minute. Cool.
Place cucumber slices and 1⁄4 cup water in a blender; process until smooth. Strain mixture through a cheesecloth-lined sieve into a bowl to measure 1 cup liquid; discard solids. Combine cucumber liquid and sugar syrup in a small pitcher. Cover and refrigerate 1 hour or until thoroughly chilled; stir in lime juice.
Place 3⁄4 cup crushed ice in each of 2 glasses. Pour 1⁄2 cup cucumber mixture into each glass. Add 1 cup sparkling water to each glass.
Garnish with cucumber ribbons, if desired.