“It felt a bit like dropping in on Mozart for lunch.” That’s how D.T. Max, a staff writer at the New Yorker, describes his first meeting with the subject of his latest book, “Finale: Late Conversations with Stephen Sondheim.”

Released in November, a year after Sondheim died, “Finale” draws on five conversations conducted between 2017 and 2019 with the composer and lyricist, whose extravagant gifts — captured in groundbreaking musicals ranging from “West Side Story” and “Gypsy” to “Company,” “Sweeney Todd,” and “Into the Woods” — made his name as sacred as Mozart’s for theater fans.

For many, this fascination extends to the personal life that informed Sondheim’s art: his famously troubled relationship with his mother, how Oscar Hammerstein II became a sort of surrogate father, how Sondheim discovered romantic partnership later in life and remained private about it.

Mr. Max, whose previous books include “Every Love Story Is a Ghost Story: A Life of David Foster Wallace,” was generally aware of such details. Yet he did not, curiously, do any further digging while preparing to interview Sondheim — for a New Yorker profile that would never materialize, pegged to a musical that Sondheim would never finish, based on a pair of films by Luis Buñuel. 

The author admits early in the book that before their first encounter, in early 2017, he did not even know where Sondheim was born, or how he got his start in musical theater; defending his intentional lack of research, Mr. Max says, “I don’t think you could do a unique Sondheim interview any other way.”

Nor had Mr. Max been the kind of diehard fan who before he met Sondheim “could tell you what happened in the second act of ‘Passion,’” one of the composer’s later works, first produced on Broadway in 1994. “There were just three or four songs of his that had been in my head for decades, that had really, really reached me. Much as I loved some other musicals, they seemed to live in a kind of funny land of make believe. His don’t.”

There were early clues that Sondheim might be less intimidating than his reputation would suggest. “When I wrote him, he personally wrote back, which astonished me,” Mr. Max says. “With most people of that stature, you either get no answer or you get an answer from a publicist or an assistant or agent.” That started a regular email correspondence, in which Sondheim “wrote back consistently and promptly. I was always shocked to see his name in my mailbox, but he liked to communicate with people directly.”

Once they met, at Sondheim’s home in the East 40s, Mr. Max was further surprised “by his affect. He wasn’t pompous at all; he didn’t hold you off. Most geniuses let you know in some way that they’re geniuses. I interviewed Saul Bellow once, and he never let me forget that he was Saul Bellow — that soon he would be back in his magical world, and I’d be writing about him. I don’t think Sondheim ever forgot who he was, but he didn’t give you that feeling. He came across more like a teacher — which is also something he did.”

The process would not be entirely harmonious, though. Mr. Max muses that Sondheim “fired” him several times during the course of their professional relationship, “though the way he fired me didn’t feel permanent. The biggest breakup came when I mentioned Andrew Lloyd Webber.” The British composer’s often critically panned but commercially successful mega-musicals established him as Sondheim’s polar opposite in the 1970s and ’80s.

Yet Mr. Max believes his in-person exchanges with Sondheim would have continued “if the work had been going well” on the Buñuel-inspired musical: “We were about halfway there.” Mr. Max was able to cull enough material for two pieces in the New Yorker’s Talk of the Town section; the first, published in 2017, also featured Meryl Streep, who was presenting Sondheim with an award from the authors’ rights organization PEN America at the time. 

The second, in 2019, followed a conversation in which Sondheim had been joined by a longtime collaborator, musical director Gemignani, and Gemignani’s son Alexander, a performer and conductor.

Mr. Max’s final impression was that Sondheim “wanted to be part of the cultural conversation. He said that real geniuses, people like Gershwin and Stravinsky and Picasso, could make changes later in life, could bring in new things from the culture. I think the most important moment for us was when he told me that he felt old-fashioned. I actually think that’s the reason he was unable to finish, or felt confused about finishing, the Buñuel piece; it wasn’t that he technically couldn’t do it, but that he was wondering, ‘Why do it?’”

On one key point, Mr. Max adds, he was wrong about Sondheim: “I thought he would be lonely. He wasn’t lonely. But it seemed to me that he could always use one more sounding board, and I think that’s the connection we had. I wasn’t reviewing or judging him; it was a loose back and forth. If the book achieves that sense of being in the room with him, that’s terrific.”