If desired, rim the edge of a martini glass with sugar. To do this, wet the rim with a lemon wedge, then dip it into sugar.
Fill a cocktail shaker with ice cubes.
Add vodka, triple sec, fresh lemon juice, and simple syrup to the shaker.
Shake the mixture vigorously for about 15-20 seconds until well-chilled.
Strain the cocktail into the prepared martini glass.
Garnish with a lemon twist.
Serve and enjoy your refreshing Lemon Drop Martini!