Without looking too hard, you'll find a few different recipes going by the name "White Lady". Two, three or even four of them are all from the same bartender, Harry MacElhone, who created the drink in 1919. His original recipe called for Creme de Menthe, Cointreau, and Lemon Juice. In "ABC of Mixing Drinks" he lists it as Brandy, Creme de Menthe, and Cointreau, and then in 1923, when he took over the New York Bar in Paris, he updated the recipe again to be gin, Cointreau, and lemon juice, which is far more palatable. Many times these days, you will find this drink made with egg white as well. The recipe used here is as it was served by Harry Craddock at the Savoy cocktail bar in London.
1 1/2 ounces Martin Miller's Gin
3/4 ounce Cointreau
3/4 ounce lemon juice
Shake with ice.
Strain into a cocktail glass.