Now, China is not in war, but, unluckily, as a Chinese, I have a lower living standard than a European, do I automatically get a chance to be let in Europe and enjoy whatever benefit the Europeans have? Since when has economics stopped working in Euroupe?

We don't choose where we are born, nor do our parents generally. We do choose how where we are born looks. Are you saying we need to move all the people on earth away from every civil war and feel responsible for that? Are we preventing civil war in our own country by bringing aggressors in? - And also not all these people being rescued are victims of civil war, many actually just have economic reasons. Many act as economic anchor for the rest of their family (they get in then later the whole family can come in).

Why explain his heritage through luck? It's not like there's a repository of souls that's randomly drawn upon everytime someone has a baby. Luck doesn't describe a causal world with a bit of noise.

It's because of the historical, and thus causal nature of the distribution of opportunity that we might have concern over the distribution.

But if we re-rolled the dice, it's not like the asian couple from around the world is suddenly going to have a caucasian baby. You being born where you were was a confluence of factors operating in a causal framework with some noise. A re-roll isn't going to make you a Hilton family baby.

Also, what a person is entitled to is a matter for society to determine. Society creates a construct that it feels is a wholesome lens or boundary, then it creates the structures to enforce it. There is no natural right to anything, including property, life, or even death (some states forbid you to choose your death). Society determines that property is useful, creates a structure to enforce it, and voila, you are now entitled to property.