Thus, we have quasi metagame mechanics that allow players to invoke the fact that their character, not the player, but the character, is lucky.
You can have lucky characters, sure, but you don't need or necessarily want characters who
invoke their own luck. In many games, such a luck mechanic requires the metagame act of the player invoking that luck on behalf of the character, in spite of it being something that the character has no control over.
As mentioned, though, there are plenty of ways to have a lucky character that
don't require granting authorship power to the player in order to work. Halfling luck (re-roll any natural 1 on a d20) was my previous example, but anything in 3.x that granted a luck bonus to a check is an example of the
character being lucky without
requiring the player to act out-of-character.
Inigo
could have a +2 luck bonus on Perception checks, or a +2 luck bonus on any checks directly related to his vengeance quest. In terms of 5E, he could probably gain
inspiration on such a check, since they tie into his motivations. There are lots of ways you
could represent this sort of thing, without needing the player to assert authorial control beyond that allowed to the character.
Given the number of viable alternatives, you really have to make a firm design decision that you
want players to have agency beyond just their characters. As a designer, you have to
want things to turn out more in line with the laws of narrative causality than with internal causality, which is a controversial decision; many people feel strongly on that topic, one way or the other.