I see what you're trying to say. But your a bit mistaken. Yes luck plays an important role but it is not only luck that garners riches.
"Half is what you know, the other half is who you know." Luck doesn't play a factor until you yourself do the work, earn your way into the right circles, then there's a degree of work before luck (you getting noticed and eventually mentorship/sponcership) before the money starts rolling in.
For the rich neighborhoods the new "wealthy" move into. While it's kind of bad to simply dislike them for how they got their riches. They have a small point. Many lottery winners don't really respect their newfound money. More importantly, they don't know how to manage it. And they buy expensive things without any thought of the cost of upkeep, repairs etc.
the rich move in certain circles such as fundraisers, charities, etc. but those who simply win their money feel that this isn't their circle and may keep themselves separate from them making them social pariahs in their new social class.
Still rather than help them(those who won the lottery) the rich just look on with disdain and that isn't good for sure.