The go-to orange accent for several drinks, including the Lemon Drop, is Triple Sec, but if you are going for a memorable cocktail, make it with Cointreau.
The result is a spirit that smells and tastes like orange but maintains a clean finish. Cointreau is perfect for a Lemon Drop martini as it enhances the cocktail's flavor.
Cointreau has light but warm spice notes, whereas Triple Sec has a flavor note of orange. Any cocktail that calls for Triple Sec would be noticeably elevated with Cointreau.
However you make your lemon drop martini, stick to the essential ingredients, and you'll always get a better result by using Cointreau for the orange liqueur.