To make the cucumber water, seed and rough chop the cucumber. Pulse in a blender or food processor with the juice of 1 lemon and about a tbsp of fresh dill. Season with salt and pepper. Strain the mixture and allow the water to drip into a shallow bowl. This will make more than enough for two martinis.
Combine about 2 tbsp of the cucumber water with vodka and shake with ice. Pour into a chilled glass.
To make the garnish, slice a thin piece of cucumber and roll with the smoked salmon. Allow the garnish to sit in the drink to add a slight flavor to the martini.