No idea hun about the lotto but my bro moved to LA about 8 years ago.
He got an internship at a company (paid rubbish wage) and then was allowed to stay as long as he was in that job.
He got sacked (they didn't like him having the poker business on the side) so was going to have to come home, but by then he was living with his girlfriend so they just got married and he was allowed to stay. They had to prove they were a 'proper couple' though.
I gather it's quite hard to get your foot in the country if there is no job waiting, etc x