When Bradley Cooper saw Lukas Nelson — next-to-youngest son of country legend Willie Nelson — backing up Neil Young on guitar at the 2016 Desert Trip festival in Indio, Calif., the actor found an oasis of inspiration for his “A Star Is Born” character, Jackson Maine.

Cooper — starring with Lady Gaga and making his directorial debut in the much-anticipated remake, opening Friday — tracked Nelson down with the help of film producer Bill Gerber, a friend of the musician’s parents.

“I knew Bradley was a big fan of Neil’s — I saw him do air guitar to ‘Down by the River’ on [‘The Tonight Show Starring Jimmy Fallon’] a few years back, and he did a great job,” Nelson — who, along with his band, Promise of the Real, plays backup for Young on tour — tells The Post. “So when he called me, I said, ‘Any fan of Neil’s is a friend of mine.’”

Thus, a bromance was born: “A couple days later, I was over at Bradley’s house hanging out, and we hit it off,” says Nelson, 29, who was enlisted to serve as a music consultant and composer for “A Star Is Born.” Then it “evolved naturally,” he says, for Lukas Nelson & Promise of the Real — who were nominated for group of the year at last month’s Americana Music Honors & Awards — to play Jackson Maine’s band in the movie.

In addition to portraying Jack’s sideman, Nelson was the main muse for Cooper’s own characterization. “Definitely he based a large part of it [on me],” he says.

But Nelson was surprised at the level of natural musicianship possessed by Cooper, who took guitar and piano lessons for his role. After hearing the actor sing the traditional folk song “Midnight Special,” Nelson felt confident that the four-time Oscar nominee would be up to the vocal challenge.

“That was really what got me,” he says. “I said, ‘Oh, OK, he can sing, too. He knows music, he knows phrasing.’ That’s how I knew.”

To keep it authentic, Nelson coached Cooper to hone his country-rock chops. “I’d sit with him every day and play guitar with him and go over songs,” he says. “I started writing songs for the movie thinking about what would sound good with his voice.”

While writing tunes such as “Black Eyes” and “Out of Time” with Cooper, Nelson also penned songs with Lady Gaga. Although the two come from different genres, they found common musical ground in their compositions, including “Music to My Eyes” and “I Don’t Know What Love Is.”

“We wrote those songs together based on our mutual knowledge of good music,” he says. “We grew up listening to the same type of thing. She’s got a tattoo of David Bowie on her arm” — and Nelson’s band covers Bowie’s “Life on Mars” on their new “Forget About Georgia” EP.

Nelson was a fan of Gaga’s country-influenced last album, 2016’s “Joanne.” “I loved that record,” he says. “‘Million Reasons’ is a fantastic song.”

And he went even more gaga for Gaga while working on “A Star Is Born.” “She’s a consummate artist across the board,” he says. “She’s an old-school type of entertainer, like Judy Garland, who just could sing her ass off and act and do it all. She’s just a superstar, a legendary person, an incredible human being.”

Clearly, the admiration was mutual: During filming, Gaga lent her background vocals to two songs on Lukas Nelson & Promise of the Real’s self-titled 2017 album, including “Find Yourself.” “She loves that song,” says Nelson, “so she came in and sang on that as a favor, and it was really great.”

Nelson has learned well about the art of collaboration over the years. He started playing in his dad’s band when he was 13, hitting the road with his outlaw father. “Mickey Raphael was my biggest mentor in teaching me how to be in the band,” he says. “Mickey is Dad’s harmonica player of 40 years.”

Meanwhile, Kris Kristofferson — who starred in the 1976 version of “A Star Is Born” with Barbra Streisand — is a longtime family friend, having played with Willie Nelson in the country supergroup the Highwaymen.

“I love Kris. He’s probably my favorite songwriter, besides Bob Dylan and Dad,” says Nelson, adding that Kristofferson supported the new “A Star Is Born.” “I think he came and visited Bradley a few times, maybe they had dinner. I know he’s proud of it.”

As for his parents — his mother is Annie D’Angelo, Willie Nelson’s fourth and current wife — they taught him some valuable life lessons. “Both of them value work and passion and dedication. And they also surround themselves with good people who are down to earth, not caught up in a lot of other bullsh - - t.”

Will Nelson’s heavy workload — some 250 shows a year — include more film gigs in the future? “My priority is music, but you never know what can happen. I could do some [more] stuff in the movie world if it feels right. I’d be happy to answer any calls about it.”