If you’ve encountered the work of Mike Birbliglia — particularly in his monologue-turned-movie “Sleepwalk With Me,” about his battle with a severe form of sleepwalking called REM Behavior Disorder — you know that he’s more than earned the right to be a little neurotic about his health.

And in his new show, “The Old Man & the Pool,” which opened Sunday at Lincoln Center’s Vivian Beaumont Theater, Birbiglia grapples with another health crisis that is even more relatable to his middle-aged NPR-listening fan base. He’s 44 now, with a young daughter he adores, and he finds himself in a doctor’s office reporting episodes of shortness of breath — and fearing that he may end up like his father and grandfather, who both suffered heart attacks at age 56.

The prescription is pretty simple: Eat better and exercise more, proposals that Birbiglia is quick to reject: “At a very early age I lost the will to push up,” he jokes, sharing stories about his awful experiences on high school soccer and wrestling teams, and a boyhood experience at YMCA pools that put him off swimming for decades.

As for improving his diet, Birbiglia seems daunted by the prospect of giving up pizza — or the convenience of junk food that’s available at all hours. “The thing about healthy food is that it goes to bed early,” he cracks.

Eventually, though, Birbiglia finds himself donning a swimming cap and baggy trunks and dragging himself to his local Y pool — where his style improves dramatically from his first day, when he “looked like what would happen if you dropped a blender in the pool.”

Instead of just doing laps around the subject of middle-aged anxiety about health and mortality, Birbiglia occasionally goes deep — in ways that suit his laid-back, self-deprecating style. (He’s the rare self-described extrovert who somehow seems more comfortable on the edge of the pool — or the curved-wave set by Beowulf Boritt that suggests both a wave and a pool’s bottom.)

Birbiglia has a way of swallowing his punchlines, of going off in tangents that circle back to hard truths, that signal his gift for shaping an overarching narrative within the confines of the stand-up form. Yes, there are jokes — like his comedic complaint about how Airbnb’s are guilty of false advertising for failing to deliver breakfast — but many serve as popcorn kernels strewn along the path to his larger point. (A point that he often then subverts with a perfectly timed punchline.) When you’re in the good company of Birbiglia, after all, it feels perfectly normal to laugh in the face of death.

Seth Barrish directs.

Read my review at TheWrap.