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.
For the sake of simplicity, let's say they aren't using a third-party for their payment needs, and will keep the Bitcoin. I would then be able to make a direct connection with the grocery store without going to any other node?
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 don't see any benefits in using LN one time only, or for testing purposes. It is good to test things to see how they work. But opening the channel requires a standard on-chain transaction with normal fees. Closing it as well. If I were to send multiple payments a day/week/month, it would make sense.
I understand that this is a a test you are suggesting. I am just saying that using LN for an one time thing doesn't save on fees or improves the speed of confirmation.