The banged-up hardcover perched invitingly on the stage of “John Lithgow: Stories by Heart” is a prop, but one with a history. Called “Tellers of Tales,” it’s a much-perused anthology of short stories published in 1939. No less than W. Somerset Maugham edited its 100 stories, which ranged from Edgar Allan Poe to Balzac to Dorothy Parker to Faulkner, and it was “kind of a Lithgow family bible” to the itinerant, close-knit, unapologetically Anglophile family that included an impressionable boy named John.

In the 55 or so years since then, Mr. Lithgow has told his share of tales himself, in a series of popular books and on CDs for children. Notwithstanding a strange period in the early 1990s when he played a series of sociopaths in glorified B movies (squaring off against Denzel Washington in “Ricochet” and Sylvester Stallone in “Cliffhanger”), he has all but cornered the market as either the sweetest goofball or the goofiest sweetheart in town. This slight but comforting stroll down story hour in the Lithgow household, directed unobtrusively by Jack O’Brien, trades heavily on this avuncular image: The imprint of his reading glasses remains visible on Mr. Lithgow’s temples as he takes the stage.

Those glasses make a few perfunctory appearances as he settles into his easy chair, as does “Tellers of Tales,” with its weathered pages and its check marks denoting favorite stories in the table of contents. But Mr. Lithgow lives up to the title of his play, reciting both a lengthy Oliver Wendell Holmes poem and an even longer P.G. Wodehouse short story — or, as he and his siblings called it when requesting it as kids, “the funny one” — without taking a glance at the pages.

This is not just to demonstrate his memorization skills or his gift for mimicry, although both are in abundant evidence. Mr. Lithgow also allows his memory to unspool in various diverting directions as he contextualizes these stories. Whether it’s reminiscing about Ina “Grammy” Lithgow, who used to recite Holmes’s “Wonderful One-Hoss Shay” in a twinkly New England brogue, or recounting the healing properties of Wodehouse’s “Uncle Fred Flits By,” Mr. Lithgow’s stories about these stories are every bit as arresting as the tales themselves. As the lights dim gradually during the 90 or so minutes, the Mitzi E. Newhouse Theater becomes the equivalent of a warm, cozy couch designed to fit 299 happily infantilized listeners, each silently clamoring for just one more chapter.

“What the Moses was coming next?” That phrase, a quaint distillation of the insistent urgency at the core of any story worth telling, can be found in “One-Hoss Shay,” an agreeably shaggy yarn about a horse-drawn buggy engineered to completely implode after exactly 100 years of use. The poem was a favorite of Grammy Lithgow, who hailed from an era when rote learning was a crucial part of every child’s intellectual and moral upbringing. (Judging from the murmurs of audience approval at each mention of these sprawling poems of the era, that sentiment remains strong among a certain generation.) And her choice seemed eerily appropriate to young John, who expected his beloved Grammy to meet with a similar fate: “Perhaps it was my first poetic insight.”

This poem, for all its hardscrabble specificity and tongue-twisting charm, is merely a curtain-raiser, though. Mr. Lithgow’s presentiments of mortality became far more concrete in 2002, when he spent several depleting weeks ministering to his father, a former theater director and manager named Arthur who was recovering slowly from abdominal surgery. Where short walks and Shakespeare trivia games failed, the comfortable ruts and grooves of narrative ultimately provided Arthur with a lifeline.

Which brings us to “Uncle Fred Flits By,” about a mischievous 60-year-old who invades suburbia, where he meets a red-faced young man who jellies eels for a living, the disapproving family of his beloved, and a parrot that glowers “most offensively” at the proceedings. Nearly half of “Stories by Heart” is given over to Mr. Lithgow’s exuberant telling of this ridiculous yarn: As he flings his strapping frame from one end of the stage to the other, embodying a half-dozen people and the parrot all at once, he tells arguably the greatest bedtime story ever told. (If, that is, the goal is to make the listener more, not less, agitated. Think of “Uncle Fred” as the anti-“Goodnight Moon.”)

The recitation would tickle the imagination under any circumstances; given its context within Mr. Lithgow’s sprightly and sensitive story, it burrows even deeper. What the Moses came next? A few extra chapters to the finite but bulging book of life, told by heart and from the heart.

Until June 2 (150 W. 65th St., between Broadway and Amsterdam Avenue, 212-239-6200).