The scan at the time of purchase is just for tracking what the store owes to the state for the lottery system. The last ticket in each roll of tickets is scanned by the dedicated lottery terminal prior to being placed for sale in an admin mode activation function. The terminals themselves I am familiar with are Linux-based and seem to be thin clients which do everything remotely in real-time, because nothing works if the terminal is offline, from activation to redemption of tickets to win/loss checking. The terminal has its own dedicated wired Ethernet connection to a stand-alone Cradlepoint or other competitor brand cellular modem/router, which along with the terminal is all outsourced to a third party management company. (SGI is the only one I’m familiar with; there are likely others.) All of this is public info which could be gleaned from observing the terminals and their installation/operation, but I probably can’t say much more about them, but they are pretty neat and seem to work fairly reliably.

Now that you mention the auditing etc, a lottery system would probably be an easy way to get people to literally buy into an online ID scheme, not because it would necessarily be privacy-preserving, which would depend on implementation details, but because a not insignificant number of folks seem to like the chance to win money. Considering many states already have lottery systems, the ID code tickets could probably be provided alongside lottery tickets for free or nearly free, and employees already have the training to check/scan IDs. If there was an incentive such as the possibility to get discounts, win prizes, or tie-in purchases of some kind, I think it could work.

Many stores that sell lottery tickets also sell gift cards, so that technology could also be used instead or in addition to ID tokens at the point of sale. There are a lot of sponsorship opportunities available for cross-promotion.

“Please drink a verification can” was probably more prescient than was at first apparent. Mike Judge saw this whole thing coming from a mile away.