As Jencks and Tach note, (hat tip: Reihan) your economic status is robustly correlated with your parent's economic status. Is it “luck” that members of the middle-class, for example, pass on middle-class virtues of hard work, the importance of investment in human capital, delayed gratification, punctuality, thrift, etc., to their children. No. Not at all.
Am I “lucky” to have been born to a stolidly bourgeouis, civic-minded, church-going police chief and nurse who filled my head with the “protestant ethic”? Simply put: no.
I don't mean to be thornily metaphysical here, but if I was not the son of James K. and Dorothy A. Wilkinson, then I would not be me. Even more to the point, if the particular germ cells that were party to my conception had been different, that being would not have been “me” with different attributes, it would have been someone else altogether. In this sense we are all “lucky” to exist at all (if existence is a perfection.) But I am not “lucky” to have the genotype that I have. I have it necessarily. That is, my genotype is not a contingent attribute of me. That a being with my genotype exists is contingent. That I exist with this genotype is necessary. The statement “I could have had a different constellation of genes” is ill-formed, not entirely different from “Gold could have had a different atomic weight.” So, insofar as any of us have “good genes,” it is not a matter of “good luck.”
Now, my manifest attributes are not simply a matter of my genes. My developmental environment will have determined how my genetic potential is expressed. So, what Dorothy Wilkinson ate, drank, and so forth while she was carrying me shaped the way I am. Am I “lucky” that mom didn't smoke? Well, Mom considered it against her religion. Am I “lucky” that Mom was a quasi-Mormon? Um. I don't know quite what to say here. But the point I'm trying to get at is that Mom did a lot of things vis a vis little me with the EXPRESS INTENTION that it have a particular effect on my welfare and character. That I have a tendency to feel guilty when I'm late for something is in part a INTENDED consequence of my mother's actions. So, from her perspective, it's not a matter of luck that I usually show up on time. It's the way she trained me.
If I meet a guy in a restaurant, and he likes the way I look, and gives me a million a year salary to work for his firm, that's luck. If I'm damn good speller, that's because I've got a good mind for words, and good training that was intended to make me a good speller, neither of which is is “luck” in any clear sense. (Please enjoy the irony of spelling mistakes herein.) We don't think it's good luck that the bridge didn't fall down when it was designed to stand up. Right?