According to the Lafourche Parish Clerk of Court ... Lana stopped by with her boat captain beau Monday and picked up a marriage license.

We're told the marriage license has yet to be returned and recorded in the records ... so, it seems Lana and Jeremy haven't exchanged their vows -- though, it certainly looks like they intend to get hitched.

Lana and Jeremy were first romantically linked back in August ... when the singer was spotted holding hands with the alligator tour guide at the Reading & Leeds Festival.

She appeared to hard launch her relationship when she brought Jeremy as her plus one to model Karen Elson’s New York City wedding earlier this month.

While the relationship may be new to the public, it's believed that Lana and Jeremy have known each other for several years.

Lana first posted about Jeremy and his wildlife tours back in 2019 ... where JD threw his arm around the pop star for a pic.

However, their relationship grew romantic around May 2024, when Lana referred to Jeremy as "my guy" in a post from a visit to Louisiana.

Lana wouldn't be the first star to marry a non-celebrity. For instance, Miranda Lambert married police officer Brendan McLoughlin in 2019, Taylor Lautner wed nurse Taylor Dome in 2022, and Matt Damon has been married to former bartender Luciana Barroso for almost 2 decades.

Still, if you ask fans, Lana is taking a walk on the wild side with this romance!!!