When you’re pondering actors associated with the indie-film company A24, your thoughts may run to the young, hot and impossibly tousled.

In years past, this stable of dewy ingénues has included the likes of Robert Pattinson, Riley Keough and Lucas Hedges. But it’s time to make way for the studio’s newest muse, a three-time Tony winner whose key roles this year in a pair of A24 films — Ari Aster’s trippy “Beau Is Afraid” and the gleefully silly “Dicks: The Musical” — offer the delightful opportunity to turn to your cool nephew and exclaim, “Oh, he’s in this?”

Rest assured, the he in question is just as surprised. “I’m now the poster boy for A24,” Nathan Lane, 67, said in a recent interview. “Who would have guessed?”

One of Broadway’s most beloved actors, Lane had his breakout moment on the big screen in 1990s studio fare like “The Lion King” and “The Birdcage,” which mined his musical-theater talents and expansive comic sensibility for all they were worth.

Although Lane has worked continually in theater and TV since, the film industry hasn’t always known what to do with him, which makes his current renaissance all the sweeter.

He was the first choice for his roles in both of those A24 envelope-pushers, even though they’re utterly unlike anything he has done before.

Take “Beau Is Afraid,” released in April, a three-hour mind-bender about filial anxiety that had Lane come in for a midmovie faceoff with an intense Joaquin Phoenix. Or sample “Dicks,” a proudly filthy queer musical that asks Lane to spit deli meat at puppets and ensures that for the rest of his life, he will share an IMDb page with rapper Megan Thee Stallion.

“Don’t you love show business, when these things can happen to a little boy from Jersey City?” Lane quipped.

The Lane-aissance could either be a feat of timing or the beginning of a trend. But it’s also a reminder, not long after Michelle Yeoh found Oscar-winning acclaim in A24’s “Everything Everywhere All at Once,” that the studio’s coolness can come from more than the minting of new stars. It can be just as rewarding to pluck well-known veterans and toss them into a world that’s unexpected and wild.

“To me, he’s the foundation,” said Aaron Jackson, who co-wrote and co-stars in Lane’s new film musical with his comedy partner, Josh Sharp. As a child, Jackson would do an impression of Lane as “Lion King” meerkat Timon to make his grandfather laugh; when he was older, he got a DVD of Lane in a film version of the 2000 play “The Man Who Came to Dinner” and watched it on a near loop.

“Now that people like us are coming of age and getting to write stuff, it’s like, what about casting one of the most brilliant actors we’ve ever had?” Jackson said.

Although Jackson, Sharp and director Larry Charles were eager to get Lane into their movie, the actor wasn’t initially sure what to make of the project. A hard-R spin on “The Parent Trap” that Jackson and Sharp based on a play they used to perform in the basement of a supermarket, their film casts the comedians as long-lost twins who conspire to reunite their daffy parents. Hayley Mills never faced such difficulties, though: Here, dear old Mom (Megan Mullally) is an eccentric shut-in with a detached vagina, while Dad (Lane) is a newly out bon vivant who’s uncomfortably devoted to the two disgusting sewer creatures he keeps caged in his living room.

“When I read it, I said to my agent and manager, ‘Are you serious with this?’ ” Lane recalled. The script had made him laugh, but he worried that the comic situations were too outrageous, even for him. To assuage his fears, Lane met Sharp and Jackson at an Indian restaurant, where their comic sensibilities clicked and cosmopolitans were served until the house lights came on.

“It went on for 4 hours, and I fell in love with them and wanted to adopt them,” said Lane, who was ultimately won over by the eagerness of Jackson and Sharp to fly in the face of decorum at a time when “Don’t Say Gay” bills were being written into law.

“We’re going to say whatever we want,” Lane said, channeling the duo’s brio. “And you’ll have to live with it.”

Still, it’s one thing to read those out-there scenes and quite another to actually perform them, as Lane found when he showed up on set. Many of his big moments revolve around those unnerving sewer creatures, a pair of diapered reptilians that his character dotes on like an attentive mama bird. (Hence the regurgitated deli meats.) Although the filmmakers considered hiring Cirque du Soleil gymnasts to play the sewer boys, they ultimately settled on two puppets, which may be an even creepier touch.

In order to play the scenes with true affection despite the twisted context, Lane endeavored to think about the sewer creatures as if they were his character’s pet corgis.

“It has to be very grounded, and it has to be subtle,” Lane said, “even when you’re spitting cold cuts at two ugly puppets in a cage.”

A more robust movie career is something Lane wants but has always been wary of: Wouldn’t you feel skittish if you gave one of the most finely calibrated comic performances of the ’90s in “The Birdcage,” and the only two film scripts you received afterward were for “Mouse Hunt” and “Mr. Magoo”?

Although Lane felt the stage could offer him a more expansive suite of roles, including his most famous part, as Max Bialystock in “The Producers,” even there, the appearance of typecasting could make him bristle. Determined to shake things up, Lane emailed a friend, actor Brian Dennehy, who was mulling a new adaptation of Eugene O’Neill’s “The Iceman Cometh.” Although that shattering drama wasn’t the sort of production he would immediately come to mind for, Lane pitched himself for the tricky role of Hickey, the salesperson who forces his bar mates to confront dreams long deferred.

Dennehy was intrigued, and the two men signed on for a production that played at the Brooklyn Academy of Music in 2015.

“It changed the way I approach everything now,” Lane said. “I wanted to be scared again. I wanted to think, I don’t know if I can do this.”

Although he wasn’t sure how “Dicks: The Musical” will be received, Lane offered some marketing suggestions. He told Sharp and Jackson that they should record a video to warn that watching the film in a theater could make the audience gay, then ask a few willing football players to serve as the guinea pigs: “You send in Aaron Rodgers and a couple of others, and then they come out of there in caftans.”

The idea was vetoed when they heard that the recent comedy “Bottoms” might also be planning a turn-you-gay marketing angle, but Lane was just happy to have the company.

“If you can get away with ‘Bottoms’ — if you can have a high school comedy about teenage lesbians starting a fight club — you certainly can have ‘Dicks: The Musical,’ ” he said.