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.
I'm about to bump my testing thread in lending so I can help with this too if necessary.
You lost me here. 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?
You could open a channel with either payment processor's node or any other well-connected node which would be able to route your payment. The routing fee should be negligible in the latter case. You wouldn't be able to connect directly to the grocery store since in this scenario, they would be using a third-party to handle your payment. Usually, payment processors offer a few different ways of withdrawing money, so the grocery wouldn't necessary need to use the Lightning Network at all.
I'm considering a payment processor might for close channels on the light Ing network too to maintain their funds so it might be interesting to see how that is dealt with (unless the funds get sent to another channel but thatight need inbound capacity - I say might because things might be changed and the ln is a decentralised protocol so they can change their own thing individually if it's just them connecting to them).