Having said that, I still think you are on point about the American Dream available for everyone willing to work hard. It just starts before you enter the US since green cards are not handed out that easily even though it is called a lottery.
Your odds of winning are something like 0.2%. If you're one of those selected I believe there's still only a 50% chance you will make it through as they select twice as many 'winners' as they have spots available. I applied for about 8 years I think without success. I then stopped after realising I had nothing to gain from moving to the US.
Also, the program is limited to persons from certain countries (for example if you like in England/Scotland/Wales you cannot apply).