How do I establish the connection to the grocery store in this scenario? I send LN payments to the node operator. The node operator opens a channel to the grocery store?
That's the "magic" of LN: the network finds a route to send your payment. As long as the node is connected to someone who (is connected to someone who) has a connection to the node you need, it should work. It sometimes fails though, but I assume that gets better over time.
If you haven't tried it yet, just try

A custodial wallet is easiest though, and if you post a payment request for 100 sats, I'll fund it so you can send a few sats to a casino to test it.