Here's my take on this subject. For those concerned, this might as well be Science vs. Faith. If you are for science, you will be prone here to say luck. If you are for faith then you are more prone to miracles. That's pretty much how this is going to work, and people's religious views will in fact intersperse themselves through this topic. In general, with regards to Luck vs Miracles, I'm going to say that nobody knows. That's the simple truth. We don't know if Jesus could magically cure people with his hands, or if he was an alien with nanobots. (Bad example, I know) We weren't there. Some of us can claim to have experienced miracles, but was it just dumb luck? For those who are versed in String Theory, you'd say that EVERYTHING is luck. (I only know a very small portion of it, so I wont be getting to deep into it.) Essentially, string theory says that there is finite probability that you take a step forward, and are suddenly on mars, and your next step takes you back to earth. This chance is so small it's not even worth considering, but a chance nonetheless. String Theory drove Albert Einstein insane in his later years, as he tried futilely to disprove it, as in his mind "No God would create a world where things could be left to 'Chance.'"
(Ftr, I do believe most medical advances and many discoveries are made completely by accident. Luck? or a celestial hand guiding them?) Even Stephen Hawking's world renowned Physicist says that we can't prove nor deny the existence of any Deity. " We cannot disprove the existence of a God, but science makes him unnecessary."
I myself am an Atheist, but one who is tolerant of religion since I was once Catholic, and understand the needs and desires for religion. So in my view. If you want to call it insane luck, go ahead, it probably was. If you want to call it a miracle, well I'll disagree, but that's your own prerogative. So long as you don't flame me, or try to convert me, or whatever, we can get along just fine.
TL;DR: We don't know, neither side can prove anything for sure. Get over it, believe in what makes you happy.