Lottery couriers are companies that will buy and scan lottery tickets for you for a fee. Most of the time, they're not actually doing much courier work. If you win a small amount, they'll cash the ticket for you and credit it to your account, and if you win a big enough amount that you have to cash it in directly with the state, they'll actually deliver you the winning ticket.
It's basically a workaround for restrictions on online lottery sales. I'm not sure how states should handle online lottery gambling—there are a lot of considerations around addiction, potential fraud, money laundering, and erosion of retailer lottery revenue and shopper base—but I don't think this is it.