Can a foreigner with legal stay play national lottery?

Most lotteries do not require that one be a resident in order to play their lottery. This allows them to attract border-crossers from states that may not have the same games (if any). Keep in mind, though, that should an out-of-state or itinerant person purchase a ticket that proves to be a winner, that person must follow the appropriate instructions to claim the prize. This usually involves either returning to the state where the ticket was purchased (either to a retailer to cash small prizes or a lottery office for bigger ones) or mailing the ticket (with appropriate claims information) back to the lottery.