Ian Alteveer, who curated the Met’s Hockney show, said he singled out the painting in the show’s catalog because it signaled a shift in the artist’s portrayal of water — from a distinct splash to a watery soaking of the canvas — and it marked the “culmination” of Hockney’s double portraits.

“It’s also a farewell to the relationship, which had come to an end,” Mr. Alteveer said, “and this grand statement about his interest in the psychology between two people that he’s been trying to capture.”

And where is the artist in the painting? Art critics have pointed out that there is little indication Mr. Schlesinger represents that title role. It has instead been suggested that the artist is Mr. Hockney himself, looking back at his lost lover, symbolically suggesting his own presence in the form of one of his iconic swimming pools.

The painting drew huge interest during the presale viewing in Christie’s Rockefeller Center showroom. “I’m only here for this,” said Post Villafane, 32, a young collector from Queens who viewed the painting on Wednesday. Mr. Villafane was not in the league of would-be bidders, but he was representative of a noticeably younger and more diverse crowd mingling with the usual middle-aged white art world insiders at this week’s presale showings. “The colors are so realistic,” he said. “They blend so well. Look how the paint shimmers. It’s beautiful.”

In reviewing the Met show, the New York Times art critic Roberta Smith described the artist’s “pictures of homosexual love and comradeship” from the early 1960s as “courageous,” given that they were made at a time when homosexuality was a criminal offense in Britain. “They should be a revelation to younger generations,” she added, “including painters using figurative styles to tell their own stories.”

The painting’s seller was not publicly revealed, but was widely reported to be Joe Lewis, a market-savvy British billionaire based in the Bahamas. He audaciously offered his Hockney without reserve, meaning he set no minimum price, a sign of how confident he was that it would sell for its estimate of $80 million. He bought the painting in 1995 from the entertainment magnate David Geffen.