To make the classic lemon drop martini, combine 2 ounces vodka with 1/2 ounce orange liqueur, 1 ounce simple syrup, and 1 ounce lemon juice in a cocktail shaker filled with ice. Shake well, then strain into a martini glass rimmed with sugar.
There are a number of other lemon drop cocktail variations to try. To make a strawberry lemon drop cocktail, add 1 1/2 ounces of vodka, a 1/2 ounce orange liqueur, 1 teaspoon sugar, 3/4 ounce lemon juice and 1 teaspoon strawberry puree into a cocktail shaker filled with ice. Shake and strain into a martini glass, then spoon the leftover puree into the martini. Stir and serve.
To make a coconut lemon drop, fill a shaker with 1 ounce vodka, 1 ounce coconut rum and a splash of lemonade. Shake well, and pour into a martini glass.
You can also make a batch of lemon drop champagne punch for a party. Add 1/2 cup sugar and 1/2 cup water to a saucepan, place over medium-high heat and bring to a boil. Remove from heat, and add lemon peel spirals from three lemons. Allow the syrup to cool completely. Pour 1 bottle of chilled champagne, 3/4 cup lemon juice and the cooled syrup into a large punch bowl, and stir. Serve with the candied lemon peels.