She has numerous aspects, ranging from aspects of war to aspects of harvests and gambling.
She is either the twin sister of Fate or - more often - Fate is another of her many aspects.
Lady Luck tampers with everything as she pleases, yet she displays a great fondness for any sort of underdogs and daring individuals or groups going against the odds. She's a singularly mercurial divine, who may or may not listen to prayers: it is thought that she derives certain pleasure from watching well-laid plans or sudden relief turn into gut-churningly terrifying failure - her clergy often depicts her as blind. She's not without compassion, but for one reason or another favours some more and some less. Those ready and willing to take risks (sometimes even recklessly) are obviously her favoured ones.
Her way of influencing the world is not entirely known, but in almost all cases it's a question of details. Who stepped on that patch of mud, exactly why did an entire military operation's logistics fail because of one single spooked donkey and et cetera. Whatever she does, she does it subtly. Luck is never vulgar and obvious.
Lady Luck is most often depicted as a classically beautiful aristocratic lady with a smile that can be interpreted as both wily and warm, curly hair (the colour varies). She may or may not have a veil covering her eyes or milky white blind eyes. She is, in fact, clothed most of the time, but the exact clothing varies on what aspect one is dealing with (aspects of fate tend to wear white togas with veils, aspects of war are often armoured).
Our lady of fortune and chance, ficklest divine
Saturnine beauty of the emerald courts, benign:
We call to you with rabbit foot, horse shoe,
Coins from the well, our sacrifices true:
Our luck has waned and our lives are forfeit.
The other gods pretend deafness
Our prayer to your ears: the desperate's rite
Before certain, ageless darkness