Wash cucumber, lemon, and mint thoroughly. Slice cucumber and lemon into thin rounds, removing lemon seeds as you go.
Bruise mint leaves by clapping them firmly between your palms or pressing gently with the back of a spoon.
Add cucumber slices, lemon rounds, and bruised mint to a large pitcher. Add any optional ingredients such as ginger or lime if using.
Pour cold filtered water over the ingredients and add ice. Stir gently to combine.
Cover and refrigerate for at least 1 hour. For stronger flavor, infuse for 2 to 4 hours.
Pour into ice-filled glasses and garnish with a cucumber slice, mint sprig, and lemon wheel. Serve cold.