Place some ice in a rocks glass or similar sized glass.
In a cocktail shaker, muddle the cucumber, dill, and sugar together until the dill is very aromatic and slightly bruised looking and the sugar is mostly dissolved.
Add the lemon juice and shrub and top with ice.
Shake well, until the shaker is very cold and is sweating.
Strain into the prepared glass, top with club soda and garnish. You can garnish with a lemon wedge or slice, cucumber slices or ribbons, dill fronds, and edible flowers if desired.