What do we mean when we say it today?
We've shortened this one. Now we just say "as luck would have it" instead of Falstaff's longer phrase. Maybe it's because we generally use luck as a positive term. Usually we're referring to good luck (not bad) so we don't want to be redundant.
Anytime we hear this phrase, it's used to mean that something good has happened by fortune or chance. Which makes sense. It's exactly what Falstaff thinks he is saying, not what the audience knows is happening.