The reason I think this is a bad idea...Person A on welfare buys a lottery ticket anyway with cash and wins $1000. This kind of transaction requires the State Lottery to get involved. They see that this person is on Welfare and denies them the $1000. Everyone is outraged.
The policy does make sense from a "you shouldn't play the lotto if you don't have the money to play it", but I'm someone who is all for much less government. This doesn't make sense from that standpoint.