I think that's reasonable and would not be surprised if the judge says that the harm placed on the individual by the state just for participating is too large, legally. But I would also not be surprised if public's right to know trumps all.

I'm not sure what the compelling public interest is in knowing the name of the person who won the lottery. I suppose there's some argument for transparency to better protect against, say, relatives of lottery officials regularly winning. But I presume there are other safeguards in place to check that things are run on the up and up.

The state gets their substantial cut--both through the lottery itself and through taxes--either way. Without having looked into the history of lottery practices, I'm pretty unconvinced that winners need to be outed to collect their winnings.