In some role-playing games, you earn Luck for accomplishing something, and you spend Luck either to accomplish something or to improve yourself so you can accomplish things. That doesn't sound like luck to me. It sounds more like experience. You don't earn luck—you're just lucky. It isn't karma. It isn't brownie points. It's just dumb luck that can happen to anyone at any time, and it can be good or it can be bad. So, maybe "Luck" isn't a good term for this kind of metacurrency. Karma is great for Marvel Super Heroes and Brownie Points are perfect for Ghostbusters, but Luck should literally be the result of actual luck, as in chance.
Luck already happens in any game with a randomizer. You roll the dice. You flip the coin. You spin the spinner. The result is pure luck. If you want a rule where you can gain Luck and use it later without stepping on the experience system's toes, you need to make sure that Luck is always acquired purely by chance.
As an example, consider any game that has a rule for critical success or critical failure. You could make a house rule that any critical success (or critical failure, or both) grants the player a point of Luck they can use later for whatever they are allowed to do with Luck. For a game with a dice pool system, perhaps there is a unique die that grants a point of Luck whenever a specific side comes up. For a card game, it's the Joker. If you're lucky, you get a Luck point.
What you can do with Luck points depends on the game, but the one thing it should never let you do is increase your skill/ability/level. That is the realm of experience, not luck. Luck that is gained should be spent on lucky breaks. Even as a resource, it should remain within its own ecosystem.
All of this has me reevaluating the metacurrency in Omnia.