May not be entirely correct, but I do believe that historically "luck" and "happiness" were much closer to synonymous.
Recall that before many of modern technological and medical advances, one's entire status and well-being was attributed to how the gods favored them. In Europe, especially, the Catholic Church took a good amount of time to ingrain in people that if they were unhappy it was the will of god. As such it makes sense that if you are a "lucky" person, you are also a "happy" person. What person who is unhappy would ever consider themselves lucky? What person who is unlucky would ever consider themselves happy?
There are suggestions that "luck" was borrowed from the German "glück" as a gambling term some time before the 15th century. This would suggest that the word "luck" originated first and "happy" derived from it. In fact, all accounts point to the fact that in English and similar languages the evolution of the word "happy" began with "luck"
mid-14c., "lucky," from hap "chance, fortune;" sense of "very glad" first recorded late 14c. Ousted O.E. eadig (from ead "wealth, riches") and gesælig, which has become silly. O.E. bliðe "happy" survives as blithe. From Greek to Irish, a great majority of the European words for "happy" at first meant "lucky." An exception is Welsh, where the word used first meant "wise."
Note the Welsh exception, proving that this isn't necessarily a rule, although for the most part a common pattern in the 10th to 15th centuries for "luck" to be equated with "happiness".