It seems to be a twentieth-century coinage. The earliest quotation in the Oxford English Dictionary is the title of a work by M. Short – “Lady Luck in 1941” – published in 1932. I don’t know anything about this author.
In 1936, in “People,” Carl Sandburg wrote “Yes, get Lady Luck with you and you’re made.”
However, the personification of Luck or Chance or Fortune as a feminine being goes back at least as far as classical antiquity: the Romans recognized Fortuna as a goddess. Somehow it seems natural for men to see Luck as a capricious woman, granting and withdrawing her favours according to whim.
