Drinks with “Lady” in the name tend to feature gin and lemon (and often egg white), in the style of the the Pink Lady and White Lady cocktails that kicked off the trend.
The Perfect Lady was created by London bartender Sidney Cox, and was the first-prize winner at the 1936 British Empire Cocktail Competition (according to English barman and cocktail historian Simon Diffords). It’s no surprise that such a light, lovely cocktail took home the honors; nor is it surprising that such a drink would continue to delight, almost a hundred years later.