The "Summertime Sadness" singer couldn't stop admiring her wedding ring Sunday while snuggling up to her new husband outside a restaurant in Louisiana.

Lana and Jeremy, who tied the knot Thursday in a ceremony at his airboat tour business HQ, sat down for a smoke break after breaking bread together ... and they appeared to snap a couple cute selfies on her phone.

It's the first time we're getting a good look at the wedding ring Jeremy slipped on Lana's finger ... the diamond looks pretty big, and it's visible from afar.

Lana and Jeremy totally look like they're in the honeymoon phase here ... and they took time to take photos and chat with some of the restaurant staff after their meal was over.

LDR certainly looks comfortable down on the Bayou with Jeremy ... and it will be interesting to see where they pop up for their upcoming honeymoon.