The German word for happy "glücklich" derives from the German word for luck "Glück". Could also be the other way round, idk.

Instead of saying "being lucky" we therefore say "having luck" instead. However, "glücklich" is commonly used in both contexts: "I bin glücklich" (I am happy) is very common as well as "Ein glücklicher Zufall" (A lucky coincidence). It's kind of implied by the language that a lucky coincidence makes you happy.

Makes sense to me that this might even be the origin of the term and the underlying emotion it described. Even hundreds of thousands years ago, people have been lucky from time to time which triggered an emotion: Happiness.