With not allowing them to buy tickets if they have an EBT card, those people will simply go to another store to only buy tickets, not letting it be known they have EBT. I could see this as wrong because they could have gotten that dollar or two from asking for change from people, thus the money they are using to buy tickets has nothing to do with the welfare system.
With not allowing them to redeem winnings, this allows middle-men to exploit those people. In the end this would help neither the state nor the welfare recipient. The same goes for if the state took money from winnings to those on welfare. In either system it will be the middle-men who walk away ahead.
I think states need to worry more about EBT going to waste in terms of people buying non-food related items and those who sell their food stamps. In the first scenario, small store owners will ring up $5.00 worth of food to someone who wants to buy a pack of cigarettes. In the second scenario, people will talk to someone who will give the EBT owner a list of items and then pay out half of what the total was. So EBT owner goes into somehwere like Ralph's, buys grocieries totalling $180 and the other person will pay out $90 (of course the ratio varies, so sometimes they'd pay out $120, just depends on how desparate the EBT owner is).
Through volunteering and simple random talks with people with EBT I've met numerous amounts of people who do those things above. And none of them buy lottery, or at least claim to not, but I think they'd fess up on that if they're willing to spill the beans on their EBT usage. NY Post also had numerous articles covering high EBT usage at bodegas, where it was likely they were trading cash for food stamps as well as high EBT-ATM usage at strip clubs and liquor stores. Most of those latter usages are people taking out money at those places to use in that place, so instead of using the money the state gives them on housing or utilities, it goes to alcohol and strippers. I think California made it so EBT can't be used in certain places, which seems is something New York should follow suit on.
I think welfare recipients shouldn't be allowed to use the money to buy lottery, but I also think the states have bigger worries than trying to stop them from getting tickets. Much more money is used towards drugs, alcohol and sex as well as is simply squandered away to people taking advantage of welfare recipients.