Make cucumber juice: Blend 1 large cucumber, then strain through a fine mesh sieve or cheesecloth to yield about ½ cup juice.
In a large pitcher, stir together the cucumber juice, lemon juice, syrup, elderflower liqueur, and gin.
Chill the pitcher until ready to serve.
Just before serving, add ice and soda water to the pitcher — or pour the base into individual glasses with ice and top each with ⅓ to ½ cup soda water.
Garnish with cucumber ribbons, lemon slices, or mint.