John Schlesinger was one of those distinctively English directors whose films defined the British zeitgeist of the 1960s. Among other accomplishments, he ushered Julie Christie onto the screen in 1963’s “Billy Liar” and coined her stardom two years later with “Darling.” But he also became hugely and smoothly successful working in Hollywood.

Schlesinger (1926–2003) had a knack for what songwriters call “the hook,” taking on projects such as 1969’s “Midnight Cowboy” or 1976’s “Marathon Man” that, like catchy pop singles, had a way of sticking in the mass imagination long after the audience left the theater.

Yet it’s easy to forget the name of his final film. It was “The Next Best Thing,” a Madonna vehicle released three years before Schlesinger’s death. The movie, which doesn’t need to be remembered, was overshadowed by the pop star’s own desire to get a rise out of the public. Her remake of Don McLean’s “American Pie,” as a promotional ploy for the film, caused a fuss when its video showed homosexual couples making out in front of an American flag.

Schlesinger, who was gay and Jewish, and came of age during World War II, must have been amused. He had already been there and done that. His 1971 drama “Sunday Bloody Sunday” made waves in its day for the taboo onscreen kiss between actors Peter Finch and Murray Head. The embrace seems nearly chaste when viewed now — certainly in light of contemporary transgressions like John Cameron Mitchell’s polymorphously explicit “Shortbus” — but marked the film as a breakthrough for what used to be called “gay cinema.”

One of four films screening as part of a two-day Schlesinger retrospective at the Film Society of Lincoln Center, the impact of “Sunday Bloody Sunday” now registers not as sensational but as a sophisticated psychological take on love.

The film, shown in a new print, is an autobiographical story about a romantic triangle: Finch’s doctor, who keeps his sexuality under wraps from his often distraught patients; Mr. Head’s shifty artist, a manipulative narcissist, and Glenda Jackson’s sexy but self-doubting divorcee. The film’s dynamic, underscored with finely attenuated tension and an acid edge, remains provocative. That’s due mostly to the indelibly British style of acting, the incisive rhythms of Penelope Gilliatt’s script, and Schlesinger’s restless mapping of interior space — a jumpiness that encyclopedic critic David Thomson finds inept. Here, at least, it seems to be an analog for the characters’ nervous systems.

No one was jumpier than Tom Courtenay as the antic fantastist “Billy Liar” (1963). The cheerfully iconic flashback to the era of kitchen-sink realism offers the flipside of the period’s more depressive dramas, about working class lads caught between the postwar doldrums and the soon-to-be swinging ’60s. Mr. Courtenay is nearly a one-man show, as Billy daydreams his way out of his meager circumstances as a hapless employee at a north country casket vendor. His compulsive need to fabricate seems less malicious than it does a necessity for survival, but becomes more complicated as would-be financers badger him for attention, and the free-spirited Liz (Ms. Christie) enters his life — symbolizing possibilities that are more than make-believe.

Lincoln Center’s series also revives the critically despised “The Day of the Locust” (1975), an adaptation of Nathanael West’s dismantling of the 1930s Hollywood myth that vaulted Schlesinger’s vision from the intimacies of his best work to the epic scale of directorial folly. Actor Willam Atherton will be present to share his experiences making the film, which was written by Waldo Salt and shot by the equally legendary Conrad Hall.

If “Locust” was Schlesinger’s big flop, then “Midnight Cowboy” is his eternal pop moment. Among other things, it mainstreamed Andy Warhol’s gay sensibility, which was dawning along with Aquarius in the late ’60s. Jon Voight plays Joe Buck, a heterosexual cowboy hustler making ends meet in seedy Gotham, while Dustin Hoffman turns in one of his signature roles as Ratso Rizzo, the declining low-life whose battle cry — “I’m walking here!” — may as well be New York City’s official slogan.

The film’s resonance exceeds its mawkish tendencies: It’s probably the only X-rated male weepie in film history. If Fred Neil’s title theme, “Everybody’s Talking” (performed by Harry Nilsson), doesn’t spin immediately to mind anytime the movie is mentioned, then surely its now-distant scenes of the neon ruckus in pre-Disney Times Square merits a wistful sigh.

Friday and Saturday (65 W. 65th St., between Amsterdam Avenue and Broadway, 212-875-5600).