Prepare the glass: Chill a martini glass by filling it with ice and water, or place it in the freezer for 5 minutes. Optional: rim the glass with sugar by dampening the rim with lemon juice and dipping in superfine sugar.
Add ingredients to shaker: Fill a cocktail shaker with ice. Add 2 oz vodka, 0.5 oz fresh lemon juice, 0.5 oz triple sec, and 0.5 oz simple syrup.
Shake vigorously: Shake the mixture for about 10-15 seconds until the shaker becomes frosty on the outside, ensuring all ingredients are thoroughly combined and chilled.
Strain into glass: Empty the water and ice from the martini glass. Strain the cocktail mixture from the shaker into the chilled martini glass using a cocktail strainer.
Garnish: Add a lemon twist by expressing the oils over the drink and placing it on the rim, or add a fresh lemon wheel.
Serve immediately: Serve and enjoy your Lemon Drop Martini while it's ice-cold.