The type of situation I could see a use for it.
Say your characters are flipping a coin or drawing a card to win the Millenium Falcon or a pile of GP. All other things being equal, it's a 50/50 situation.
Now, you could just flip a coin. But what if your character was a naturally lucky one? Or naturally unlucky?
So instead of that, both participants roll on their Luck attribute and the highest wins. If they have the same Luck attribute, it's still 50/50. But if one has a higher Luck attribute, the odds change in their favour.
It only works if you Luck in your world is a thing. If there's a god of Luck, or Fate is a force of some kind, or there really are lucky and unlucky people. You have to buy into that fiction. But in an RPG that's easy enough.