The music business has never quite known what to make of Gary Lucas. Go to a site for streaming or downloading songs, and you may find his music consigned to a vague category called “other.” Look him up in standard reference works, and he’s likely to be referred to as a “legendary left-field guitarist” whose work is “eclectic” or just plain “eccentric.”
“I like and like doing all kinds of music, and that’s been a blessing and a curse, but I’ll accept that,” Mr. Lucas said in a recent interview, in advance of the release on Tuesday of “The Ordeal of Civility” (Knitting Factory), his new CD. “There’s probably not a genre you can think of that I couldn’t find an example of something worthy in it. I look at myself as a global citizen: it’s a big old world out there, and I don’t want to be restricted.”
For much of his career, Mr. Lucas, 58, has also operated out of the spotlight, initially as a guitarist in the resolutely avant-garde Beefheart ensemble and later, in the early 1990s, as the writer of a dozen songs with Jeff Buckley, the best known of which are “Grace” and “Mojo Pin.” But among music professionals, he has long been held in high esteem for his dexterous and inventive playing.

For the last 20 years, perhaps the only constant in Mr. Lucas’s musical life has been the rock group he leads, Gods and Monsters, which includes members of Television and the Modern Lovers and is scheduled to perform at Joe’s Pub on May 27. “The Ordeal of Civility” is meant to be radio-friendly and, without forcing Mr. Lucas to relinquish his guitar frolics, finds him singing more and incorporating horns into his sound to a greater extent than in the past.

In addition to performing on electric, with an assortment of pedals, boxes, slides and other effects to distort his sound and create delays and loops, Mr. Lucas also plays acoustic guitar extensively, his favorite being a steel-body National of the sort favored by bluesmen. But in both formats, he strives for a sound that might be called music from the Delta — both the Mississippi and the Ganges.

“Gary’s music has a particular kind of defined strangeness that works well because it is so completely open-ended,” said Jerry Harrison, the former Talking Heads keyboard and guitar player who produced the recording and has occasionally toured with Gods and Monsters. “He’ll use unusual tunings and chords that you don’t normally see in rock music, often in a sort of modal or dissonant nature that challenge the musician to play along with them.”

One recent recording, “Rishte,” is a collaboration in that style with the Muslim Anglo-Pakistani ghazal singer Najma Akhtar. Another project, “The Edge of Heaven,” is a bluesified rendering of mid-20th-century Chinese pop songs; Mr. Lucas has also made several records, among them “Busy Being Born” and “Street of Lost Brothers,” which draw on Jewish themes and traditional styles like klezmer.