By this time, fans were demanding new music from Lorde with mounting impatience on Twitter, Instagram and Tumblr. In no mood to rush things, she tried to tune these voices out — but it was reassuring, all the same, to know that they still cared about her.

In March of this year, Lorde finally released the first single from “Melodrama,” called “Green Light.” The opening couplets follow a jarring AABC pattern, but the most striking feature is a dramatic key change, arriving just before the chorus, that feels like a small sun rising — out of place but grand. Two nights before our trip to the Flame, Lorde performed “Green Light” on “Saturday Night Live,” and when she broke into a suite of winningly uninhibited dance moves, her sequined top shuddered and sparkled like a disco ball. Later she sang a piano ballad called “Liability,” about how being an artist in the public eye can make you radioactive to those close to you. She delivered this song almost motionless on a piano bench, wearing an antique-lace-accented ensemble and floppy matching headpiece. (She wanted to look like a moth.) In a month she was scheduled to perform at the Coachella festival in California, and in between the 11th-hour “Melodrama” studio sessions in New York, she was in frequent communication with a production designer, figuring out what that show, and a subsequent tour, would look like.

Taking quite so much time on “Melodrama” was never Lorde’s master plan. (In July 2014, a member of her camp spoke hopefully to me of an “early 2015” release date.) But follow-ups are hard to make and can be especially vexing when they follow smash debuts. For three full days before “Green Light” came out, she said: “I couldn’t get out of bed. I didn’t want to be out in the world. It was so intense to arrive at this moment of, This is it.” And, she added, “whatever it is, it’s about to be out of my control.”

Lorde, whose real name is Ella Yelich-O’Connor, was born in 1996, the second of four children; her father, Vic O’Connor, is a civil engineer. Her mother, Sonja Yelich, is an award-winning poet whose work has been anthologized multiple times in the “Best New Zealand Poems” series. Ella was a bookish kid. She led her middle-school team to a second-place finish in the 2009 Kids’ Lit Quiz World Finals, a global competition. Shortly afterward, she sat for a morning-show interview on Radio NZ, estimating that she’d read “a bit more than 1,000 books” in her lifetime. She wrote her own fiction too, enamored of Raymond Carver and Kurt Vonnegut. When I asked her to characterize this work, she said only, “It wasn’t very good.” Sonja Yelich told me that when Ella was 14, she proofread Yelich’s 40,000-word master’s thesis: “People said, ‘You’re crazy to entrust this massive undertaking to your child.’ ” (Yelich has routinely accompanied Ella on her travels and is as much confidante as chaperone. You can see her dancing beside Taylor Swift in a 2014 awards-show cutaway as her daughter performs.)

Ella joined student musicals and began performing acoustic Amy Winehouse and Kings of Leon covers around Auckland with a friend named Louis, who played guitar while she sang. In August 2009, Louis’s father emailed a recording of the pair performing Duffy’s “Warwick Avenue” to Scott Maclachlan, an A.&R. executive at Universal New Zealand. Maclachlan wasn’t looking for a guitarist, but Ella’s voice intrigued him. He signed her to a development deal and worked, until a couple of years ago, as her manager. He told me that, early on, he “had very traditional A.&R. ideas of finding songs, finding a producer and putting them all together” — but Ella, whose sense of self was too strong to submit to others’ writing, chafed. “After a couple years,” Maclachlan went on, “we got to a point where it was, like, well, write something yourself. So she did. It was a little clunky, arrangement-wise, but the lyrics were really good. And if that’s working, everything else is fixable.” Ella’s precocity helps to explain the wave of Lorde Age Truthers that arose after “Pure Heroine,” with people speculating, tongue only partly in cheek, that she must be a grown woman. In 2014, The Hairpin obtained a birth certificate confirming that Lorde was, as she claimed, a teenager.