Pour 1 to 2 tablespoons of sugar onto a small plate. Moisten the rim of a martini glass by rubbing with a lemon wedge. Dip the rim of the glass into the sugar to coat.
Pour lemon juice and simple syrup into a cocktail shaker filled about half full with ice. Cover and shake vigorously for about 15 seconds.
Strain into the prepared martini glass. Pour in the club soda. Garnish with lemon twist (optional).