The science fiction writer Larry Niven supposed (at least in his fiction) that if luck were heritable, you could breed for it. And in his universe, that's exactly what happened: the Pierson's Puppeteers, a race of paranoid manipulators, distantly pulled the strings of Earth's politics. When Earth had become overpopulated, the world government instituted a lottery. You couldn't have kids unless you won. So if luck was heritable, the human race would become luckier. They did, eventually serving as a counterbalance to (luckily) win wars against the kzin, who have been described as Klingons that look like bipedal tigers. In fairness the kzin are cooler.
Of course in one sense this is a silly idea, even beyond the idea of there being a "gene" for luck. All of evolution is a game of chance, with a few adaptations that skew the odds. No living thing would be here today if its ancestors hadn't been lucky.
But there's a far grislier frame in which the idea has been explored. The Spanish film Intacto is about people with supernatural luckiness; they're even able to steal others' luck. Max von Sydow is always good but the film spends too much time on European cinematography tricks and not enough developing the idea (nb, if you like cinematography, don't write this film off on that basis - I like the ideas and don't care what it looks like. To auditory-learning bastards like myself the book is always better.) It's eventually revealed that von Sydow's character learned of his extraordinary luck when he was living in a German prison camp, and the people around him were executed one by one. He was the last - and of course, that's when the Germans abandoned the camp and the Allies came.
Art imitates life even without trying. Der Spiegel tells the story of a still-living Auschwitz inmate: "When they had no more use for [Yitzhak Ganon], the Nazis sent him to the gas chamber. He survived only by chance: The gas chamber held only 200 people. Ganon was number 201. On January 27, 1945, Auschwitz was liberated by Soviet troops." Read more about Ganon's story here.
It's an odd feeling to be one person away from (in)famous people. A physician who came to talk to my med school class was imprisoned at Auschwitz when she was a little girl, and while she was there she met a doctor who gave her candy. The following sentence may seem frivolous but it doesn't feel that way to me. If we can play six degrees of Kevin Bacon with the people we meet in our lives - and that seems a more meaningful version than movies - this means that I'm only one person removed from Josef Mengele. If reading a blog counts, you're only two.