Based on my experience, I think probably 20-30% of the American workers really care - and they will do their jobs well regardless of the reward or compensation they get. It is their duty and they will do it. My own organization shines because of them but these are just shining spots.
Then there is probably 10% that just don't care no matter what the reward or punishment is.
Now, how do you manage the other 60%-70% whose behavior can range from "going through the motions" to "going above and beyond"? This is where the customer gets consistency and excellence. I am pretty sure a lottery system won't help as much as a well defined system to motivate.