Combine 3/4 cup water and sugar in a small saucepan. Bring to a boil; cook until sugar dissolves, stirring occasionally. Remove from heat; cool.
Place sugar mixture, diced cucumber, lemon juice, and ginger in a blender; process until smooth. Cover and chill.
Combine cucumber mixture and sparkling water in a pitcher; stir gently with a whisk until blended. Serve over ice; garnish each glass with a cucumber spear, if desired.