Gary Lucas outside the West Village studio where he used to rehearse with Captain Beefheart in the late 1970s. Melanie Burford/Prime for The Wall Street Journal

Don't typecast Gary Lucas too readily. His wizardly way with the guitar, avant-garde affinities and ever-present felted beaver-fur hat might stamp him as the definitive New York art rocker. He's got the bona fides, dating back to his formative early-'80s stint as a guitarist in the last edition of the Magic Band, the alchemical engine for the late rock 'n' roll visionary Captain Beefheart—whom Mr. Lucas also managed.

"I don't mind being categorized as an experimental player," said Mr. Lucas, 56 years old, over morning coffee at the home of a friend near his West Village apartment. "But I've written songs that have been Grammy-nominated. How many people out of that scene really have made any attempt to bridge a gap, to try to expand the audience to include people who normally might reject avant-garde music?"

The guitarist's award-worthy collaborations with singers Joan Osborne ("Spider Web") and the late Jeff Buckley ("Grace") are only the best known of his musical allegiances, which also include albums devoted to 1930s Chinese pop songs, original soundtracks for silent films, and studio summits with the Dutch minimalist and lute player Jozef van Wissem.

While looking ahead to the May 10 release of "The Ordeal of Civility," a new album with his band Gods and Monsters, and a release party Saturday at the Knitting Factory in Brooklyn, Mr. Lucas was racking up his frequent-flyer points.

Not long home from a show in Kraków, Poland, he would soon be returning to Havana, Cuba. There he's engaged in his latest project, working with two leading Cuban pop vocalists—sisters Haydee and Suylen Milanes—and Los Van Van, the country's premiere post-revolutionary dance band. The swinging polycultural fusion effort, assembled by Toby Brocklehurst of Cloud 9 Productions, is a world away from the driving rock of Gods and Monsters. "I am totally psyched," Mr. Lucas said, noting that they've worked up a tropicalized version of "Satisfaction," as well as an update of "Yolanda," a song made famous by the sisters' father, Cuban music legend Pablo Milanes. "This is just about the most exciting recording project I've ever been involved with."

This week, at least, Mr. Lucas is in more familiar mode, fronting Gods and Monsters, a band he put together in the early 1990s, with rising star Mr. Buckley as a vocalist. The name is inspired by an ominous toast made in the 1935 horror classic "Bride of Frankenstein: "To a new world of gods and monsters!"

"We used to play a recording of that at every show, and then go into a metal version of 'Ride of the Valkyries,'" Mr. Lucas recalled, acknowledging the absurdity. "We like to have fun." The songs on "Ordeal" live up to that goal, and do, indeed, feature a tune devoted to a comic-book creature (the stoic, rollicking "Swamp T'ing"). And Mr. Lucas's virtuosic playing, with its mercurial flashes of Delta blues and cosmic skronk, shares a fuller soundscape. Aided by the production skills of former Talking Heads member Jerry Harrison, keyboards and horn arrangements bolster the group's stalwart bassist Ernie Brooks and drummer Billy Ficca.

"It's always a wild ride with Gary," said Mr. Brooks, who first played on the guitarist's 1994 album, "Bad Boys of the Arctic." "He charges through the songs and we're there trying to nail it down. He plays in such a unique way. You can usually watch a guitar player's hands and know if it's a B-minor chord. With Gary's fingerings, it's impossible. He has tunings no one else seems to use."

Mr. Lucas's grounding in traditional American guitar forms shows up on the instrumental "Whirlygig," which also describes the sensation evoked by his fleet playing, while the bluesy, hard-bitten braggadocio of "Peep Show Bible" should satisfy any Beefheart loyalists. Those ranks still include Mr. Lucas, who has been hosting occasional seminars dedicated to his former mentor, also known as Don Van Vliet.

While en route to a performance at the Havana Jazz Festival last December, Mr. Lucas was surprised when some familiar lines popped into his head. "The stars are matter / We're matter / But it doesn't matter," he recited. The musician first read them on the back of Mr. Van Vliet's 1972 album "The Spotlight Kid." "I used them in an epigraph in my Yale yearbook, next to a picture of me wearing a robot mask," Mr. Lucas said. "I thought he was a great poet." The next day, Mr. Lucas got a text message informing him that the Captain had died. "I was shocked. It was like I was getting a message from him as he was leaving the planet—whatever happens, don't sweat it. Life is for living. You might as well enjoy it."