Anthromorphisim of stocastic process.
Given female persona as most people who indulge in the whims of chance are male.

An imaginary female character to be appealed to for protection from mishap when one knows he (or she) is taking a risk. Sort of like asking Athena for guidance or protection I guess.

For example: "let's hope Lady Luck stays with us on this one..." or "Lady Luck, don't fail me now!".