Pour the turbinado sugar on to a small plate.  Combine the first four ingredients in a shaker and shake until the sugar dissolves.  Add some crushed ice to the shaker and shake well to cool the martini.  Rub a lemon wedge on the glass and dip the edge of the glass into the turbinado sugar to coat as if it were a margarita.  Strain the drink into the glass. Garnish with a slice of lemon.