Place four glasses in the freezer to chill while preparing the drink.
Process the cucumber using a food processor with a grating blade. Alternatively, blend chopped cucumber in a high-speed blender until pulpy.
Transfer the grated cucumber into a fine mesh sieve set over a bowl. Using your hands or a spoon, press and squeeze the cucumber pulp to extract as much juice as possible. You can also place the pulp in a muslin cloth and squeeze firmly.
Measure out about ½ cup of the cucumber juice for the slushie.
Add the cucumber juice, fresh lemon juice, gin, elderflower liqueur, sugar syrup, and plenty of ice to a blender.
Blend until the mixture reaches a smooth slushie consistency. If needed, add more ice and blend again.
Taste the mixture and adjust sweetness with extra sugar syrup or tartness with more lemon juice.
Pour the slushie into the chilled glasses.
Garnish with thin cucumber ribbons or rosettes threaded onto cocktail sticks and serve immediately.