I think part of the problem with realistically viewing one's life through this prism is the impossibility of determining what percentage of one's success is due to luck. In a sense, literally everyone who is alive today is lucky. They are the product of an unbroken line of genetic material passed down for millions of years. Can you imagine? Not one of their thousands and thousands of ancestors managed to be killed be…
And if you recursively click the first link in Wikipedia articles, you end up at philosophy :) My point is that if you dedicate a lot of time thinking about any particular aspect of life, you end up back at the "Getting to Philosophy" problem. Your luck comes in shades of grey. At some point, the line between black and white is drawn rather arbitrarily. Would I consider myself "lucky" to be born in the US? To be born…
As a person, I find it useful to consider how I've been lucky in that a) I'm better able to take advantage of the luck I've had, and b) it makes me more careful about downside risk. It also helps keep me from a certain fat-headed overconfidence. As the line goes, "Some people are born on third base and go through life thinking they hit a triple." I think that stunts people's growth.
As a citizen it's especially important for me in figuring out how to vote and what to advocate. I'm a big believer in the veil-of-ignorance approach: [1] In helping design a society, I should do it so that I would think it fair no matter which role I played. You can look at that as a way to subtract luck from the equation.