Great questions. Philosophers have been concerned about the role of luck or, as it is sometimes referred to as fortune. Among Ancient philosophers such as Aristotle attention was given to the extent to which a person's character and flourishing depended on luck or, putting it differently, depended on factors outside a person's control. There was concern for what a contemporary philosopher calls "the fragility of goodness." To get to your questions we have to share an understanding about what is meant by 'luck.' Presumably a person is lucky when she is the benefit of some good that she did not deserve. This might be through chance or through some other agent. In this sense, being born might be considered a matter of luck for, unless we are to appeal to Karma and a robust account of reincarnation, it appears that none of us can take credit for being born nor for our fundamental powers and opportunities. In a religious context, this might be thought of as grace. Apart from this major,...

Interesting points. I take it that the most reasonable reply for a defender of the ontological argument to make is to claim that Prefoessor Smith's world is not in fact possible. If one can make a case for abstracta (properties or propositions necessarily existing) then there cannot be a world where only a single pencil exists. For a good case for such a Platonic position, see Roderick Chisholm's Person and Object. R.M. Adams also has a good discussion of the difficulty of imagining / conceiving of God's non-existence. I take this up in a modest book: Philosophy of Religion: A Beginner's Guide (Oneworld Press, Oxford) or in more detail in a discussion of Hume and necessity in Evidence and Faith: Philosophy and religion since the seventeenth century (Cambridge University Press).