Without looking too hard, you'll find a few different recipes going by the name "White Lady", two, and perhaps 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. I've also seen reference to him listing this drink with egg white as well.
The recipe I am listing here, is as it was served by Harry Craddock at the Savoy cocktail bar in London.
Shake with ice. Strain into a cocktail glass.
Source: Harry MacElhone, New York Bar in Paris, ~1923