From 1984 to 1989, everyone in downtown New York wanted to be John Lurie. Or sleep with him. Or punch him in the face. Lurie, the star of the Jim Jarmusch films “Stranger Than Paradise” and “Down by Law” and the saxophone-playing leader of the jazz-punk group the Lounge Lizards, was droopy and skinny and intensely charismatic. His “Down by Law” co-star, Roberto Benigni, described him in his fractured English as “a very big actor and musicist that in the world everybody know . . . between Ray Charles and Brigitte Bardot.” Lurie wore a Borsalino fedora and old suits and painted expressionist album covers and picked up girls at the Mudd Club and snorted coke at the Palladium with Steve Rubell and Rick James. He got addicted to heroin, but kicked it; he got hepatitis, but kicked that, too. He was young and cocksure and he wouldn’t truckle. Between Fourteenth Street and Canal—the known universe, basically—he was the man.

In the nineties, Lurie became less cool but more interesting. He mouthed off to Woody Allen and Barry Sonnenfeld and let his acting career go. His money disappeared, of course, but he co-wrote Conan O’Brien’s “Late Night” theme song, and his “Get Shorty” soundtrack was nominated for a Grammy. He made a beguiling album that purported to be the influential blues stylings of a half-Jewish, half-African mental patient named Marvin Pontiac. And “Fishing with John,” a tongue-in-cheek cable show about his fishing trips with wild men like Dennis Hopper, showcased all his ingenuity and lacerating candor. Tom Waits got so mad at Lurie during their trip that the two stopped speaking. Matt Dillon complained about his episode, Lurie recalls, saying, “You made me look dumb.” “No,” Lurie replied. “God did that.” (Dillon says that he doesn’t remember the conversation.) And so ended that relationship, too.

At the conclusion of an ice-fishing episode co-starring Willem Dafoe, the narrator announced that both men had starved to death. In fact, Dafoe is still alive and still speaking to Lurie—or in theory still speaking to him. A year and a half ago, at the age of fifty-six, Lurie disappeared. Dafoe said, “Maybe this reclusiveness is his way of continuing to try to make sense of things—you could never separate John’s work from his personal challenges.”

What happened first was that Lurie was stricken with a mysterious disease that confined him to his SoHo apartment for six years. Then, in 2008, he and his closest friend, a younger artist named John Perry, had an explosive rupture, and Lurie went into hiding, believing that Perry intended to kill him. There were certainly grounds for concern, as Perry was stalking him and saying things like “Scumbag, one day you’ll be gone and this earth will be delivered from the virus of your existence.” Lurie’s improvised witness-protection program has taken him from the island of Grenada to a house in Big Sur, California, belonging to his friend Flea, of the Red Hot Chili Peppers, to an obscure village in Turkey. In October, Lurie began living incognito in a rented house in Palm Springs, California. He keeps a ninja baton and a can of pepper spray by his bed, and only seven people have his new cell-phone number. He calls them late at night, asking, “Can I come home?” There is no easy answer.

One day in June of 2002, Lurie worked out hard to prepare for an expected nude scene in the HBO prison drama “Oz.” Afterward, he went to the West Village restaurant Da Silvano, still thinking about ways to enhance his appearance—“I wanted to make my penis look enormous onscreen”—and suddenly the world was spinning violently and he couldn’t move. “I had never been afraid to die before,” Lurie said. “I had always thought either you go to the light or it fades to black. But now this creepy, ignoble, wormlike force rose up in me, saying, ‘I don’t want to die! I don’t want to die!’ ”

The following weeks brought a cascade of strange and overpowering symptoms: flashing lights and roaring sounds, a sensation like rain pouring on his skin, a Kryptonite-like reaction to Windex, an inability to hold so much as a skillet in his left hand. His condition was diagnosed as multiple sclerosis, epilepsy, and about ten other things, including postural orthostatic tachycardia syndrome, or POTS, a verdict he resented because its acronym was so lame. Lurie finally came to believe that he had chronic Lyme disease—a condition whose very existence, as he wryly acknowledged, was fiercely disputed in the medical community.

He often couldn’t leave his apartment, let alone play an instrument. When he felt up to it, he worked on his memoirs, and he did some voice-overs, hawking Toyota Tacomas in his growling baritone. He also began painting again, taking it more seriously this time. Lurie soon had a number of solo shows; as his canvases began selling, for up to fifty-five thousand dollars, the Times proclaimed that “music’s loss may turn out to be art’s gain.” He’d move among four paintings at once, constructing vivid, childlike scenarios around the topics of sex, perplexity, God, and bunny rabbits—treating his brush the way he used to treat his saxophone, as if he’d just found it on the street. If the horse he’d painted had a mane that was way too short, he’d save the painting by titling it “Horse with Mullet.”

But much of the time he just lay on his green couch, smoking and wincing at the slightest noise. During this period, the person who seemed most in tune with Lurie’s needs—other than the bar owner who came by faithfully with fried chicken from Blue Ribbon—was John Perry. Perry was a six-foot-three, two-hundred-and-five-pound former college decathlon standout who rode a Kawasaki, knew judo, and cut his own hair. Capable and engaging, he had a soft voice and a deliberative manner, like a bear awakened early from hibernation. He lived to paint portraits and still-lifes, and only when he received the occasional eviction notice from his seven-hundred-dollar-a-month apartment on the Upper East Side would he put in a few days as a construction worker or a substitute teacher, keeping the anxious, scroungy details, like much of his private life, to himself.

Perry and Lurie got to know each other in the early nineties, at the SoHo restaurant Lucky Strike, where they both played in the back-room poker game. Lurie was a voluble half-Welsh, half-Russian-American Jew, and Perry a reticent half-Korean, half-Lithuanian-American Jew, but there was an instant affinity. Soon, they were playing pickup basketball with a group of bouncers, night-club managers, and drug dealers, most of them black and a decade or so younger than Lurie—warriors who did battle on the playground before sunrise, while lesser men were sleeping on percale sheets.

Lurie said, “After I got sick, my artist friends, except for Flea and Steve Buscemi, fled from me. And then I had my tough-guy friends, where the biggest guy would take the biggest piece of chicken; they didn’t believe in evolution, let alone an internal life. John was both, but he really had my back, and I loved him. He seemed like Abraham Lincoln, the most decent, thoughtful person.” Perry told me that Lurie was the only one he could talk to about his feelings of depression and misgiving, the only one who not only wouldn’t think him weak but would respond with his own uncertainties.

The men had several extended breaches, over such questions as who failed to read whose autobiographical writings fast enough, but by the summer of 2008 Perry was again Lurie’s mainstay. He taught him how to paint in oils, set up his new Apple computer, gave him a 3 A.M. haircut, and dropped by three nights a week to play cutthroat heads-up poker for a couple of hundred dollars. Lurie’s girlfriend, Jill Goodwin, said, “I’d be with John at 2 A.M., and then John Perry would show up, and I’d be pissed.” When Perry left the apartment, he’d say, “Ganbatte,” a Japanese word meaning, in his loose translation, “Call on your fighting spirit.”

Lurie knew that Perry’s stoic countenance masked some turbulent impulses. In 1999, a bouncer at a club called Life beat Perry up after he got into a drunken scuffle. Perry, a frequent drug user at the time, quit pot and cocaine for a week, readying himself. Then he returned to the club on a Saturday night and dove over the ropes, getting the bouncer in a choke hold before the other bouncers beat him down. Perry was arrested for assault and sentenced to a day of community service, washing sanitation trucks in Central Park. A few years later, he fought off two men who broke into his apartment, apparently looking for drugs, beating them with the weapons at hand in his kitchen: a machete and a flute. In 2008, he was arrested for using a baseball bat to bar two off-duty cops from looking at a vacant apartment in his building.

Early in their friendship, when Lurie played the as yet unreleased Lounge Lizards album “Queen of All Ears” for Perry, he was surprised to see tears rolling down his friend’s cheeks. “You really are an artist,” Perry said. “What am I going to do if I hear that in public? I can’t be seen crying.” In October, 2008, Lurie took Perry out to lunch for his forty-third birthday, and Perry suddenly remarked, “I don’t think I’ll be able to stand it when you’re dead.” “I’m going to live way longer than you,” Lurie replied.

Despite Perry’s admiration for him, Lurie told me, “John never hung on my coattails like other people did—I really felt we were equals.” Perry’s independence was both a comfort and a provocation to Lurie, who, like many middle-aged artists, kept himself vital by seeking out younger friends and lovers. (Jill Goodwin is thirty-one.) Perry told me, “It would be natural to assume that we all felt John was the man, the way he had been, but the truth is that, downtown, we”—the club-hopping buccaneers Perry hung out with—“were the famous ones, in a sense, and John was like our little brother.” Perry said that he and Lurie sometimes competed for women—“John was older, but he could be funny with girls, and if they knew his celebrity that always helped”—but added, “I didn’t need John to get in anywhere, or to get laid. There was nothing John had that I wanted, except more recognition for my work.”

In the fall of 2008, Perry asked Lurie for a favor. The younger artist was going to make an instructional television pilot titled “The Drawing Show,” hoping to interest PBS in airing a series that would raise his profile. He asked Lurie to pose for him, and though Lurie had been turning down film work for years—the strong lights inflamed his symptoms—he agreed, and even offered to help pay for the shoot. (Although Perry was flat broke, he declined, not wanting to be further beholden to Lurie, and borrowed the necessary six thousand dollars elsewhere.) On the evening of November 8, 2008, Perry brought a five-man crew to a friend’s apartment near Gramercy Park to film his and Lurie’s collaboration.

Footage from the beginning of the shoot shows the two men facing each other, handsomely framed, with Lurie beside Perry’s easel. Each had a shaved head, and each looked keen and attentive under spotlights that left a well of darkness between them. As Perry roughed out Lurie’s face with charcoal, he explained what he was seeing—“His left eyeball, which is to my right, is a little bit lower than his right one”—and Lurie pursed his lips, then smiled. He had told himself to suppress his natural inclination to take over, but when Perry lapsed into silence, absorbed in depicting what he saw, Lurie would prompt him by asking why he closed one eye, or what he was using the eraser for. Perry’s observations about composition and technique were apt and intriguing. You could see how, with editing, there might be a show in the idea. But some of Lurie’s sallies tried Perry’s patience:

LURIE: The name of the show is “How to Pose”? PERRY: That’s right. LURIE: That’s good. “Be a Poser”? PERRY: I wouldn’t go that far. LURIE (a beat): Why do I feel like you’re putting a pig’s nose on my face?

When Lurie arrived, around 6:30 P.M., he had been struck by the crew’s indifference to him. Celebrity is the power to rivet attention, and Lurie realized that his riveting faculties had lapsed. He told Perry, “When I went into my house, I was famous—I come out six years later and nobody knows who I am,” meaning it as a cultural observation: I am Rip Van Winkle, returned but unknown. Perry thought the remark seemed self-involved, as did Lurie’s asking him, “Am I going to get out of here by ten o’clock? I have an appointment to get laid.” (He and Goodwin were not then together.)

Lurie now regrets the crudeness of the remark, and told me that when Perry looked stressed out he called his date, a librarian, and cancelled. As it happened, the shoot ran long and took a toll. A few hours in, Lurie was clearly ill, wincing and slumping in his chair. Sweat bloomed on Perry’s forehead as he eyed his model—“You’re doing great”—and haltingly explained to the cameras why he was erasing his original lines and hatching in subtly different ones: “It’s really the essence of drawing—to separate what you think is there from what is actually there.”

Around 10:30 P.M., in the middle of a take, Lurie, who by now felt as if bees were stinging him all over, said, “I really am in agony. I just—I can’t handle it. You’ve got to figure out how to make it shorter.” Perry looked stunned. “How much longer?” Lurie asked, head down. “I could use another fifteen, twenty minutes,” Perry replied. After a moment, Lurie said, “Let’s just keep going.” As Perry raced to put on the finishing touches—mouth, cheek, shirt—the portrait grew fuzzy and self-doubting.