Luck Attribute in TTRPGs

Adding Luck as a combat-related attribute is an idea I am toying with for my TTRPG.

The idea is at its infancy and so far I am only thinking of Luck attribute as providing Luck points which can be used for re-rolls. It's simple and doesn't break the game apart but it feels flat. I am looking for a more creative approach and the one I am considering is that players would have Luck points and if they wished to use them for re-rolls, they would have to offer a consequence (such as dropping a weapon or being knocked down) but if their re-roll is successful, the consequence will not occur.

Anyway, I would love hear other ideas. Have you come across satisfying Luck mechanic resolution in some games?