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Forty years ago, Lily Tomlin made her film debut in Robert Altman’s “Nashville,” surprising those who knew her only from her array of wacky characters in “Rowan & Martin’s Laugh-In.” As Linnea Reese, a gospel singer and mother to two deaf children, Tomlin gave a performance that was layered and fascinating. “At that time, actors weren’t really crossing over from television,” says Tomlin. “Goldie (Hawn) had done it, but that was a rarity.”

But the role almost never happened for her; Louise Fletcher, the daughter of deaf parents, had to bow out. In the end, it put Tomlin on the map, launching a film career that would include such classics as “All of Me,” “9 to 5” and “Big Business.” It also earned Tomlin her first Oscar nomination.

I specify “first” because Tomlin is back in the mix this year for her raw, funny, furious portrayal of the title character in Paul Weitz’s “Grandma.” Tomlin plays Elle Reid, a respected but broke poet whose 18-year-old granddaughter Sage (Julia Garner) needs $600 for an abortion that same day. The two spend the day visiting various people from Elle’s life in an attempt to raise the funds. The film premiered to raves at this year’s Sundance Film Festival, generating Oscar buzz for the 75-year-old Tomlin.

Weitz, who directed Tomlin in 2013’s “Admission,” wrote the role with Tomlin in mind; something the actress says was both flattering and intimidating. “I don’t know if any director has done that for me before,” she admits. “But there was a moment of, ‘Oh, I hope I like it!’”

Tomlin needn’t have worried; she was instantly taken by Elle and signed up for the no-frills shoot, which clocked in at 19 days on a budget of less than $1 million. “But it never felt like we were moving too fast,” Tomlin says. “People ask if it was a hard shoot, but it never felt hard because I was working with amazing people and doing a script I cared about.”

Tomlin’s contributions didn’t just stop with acting; the 1955 Dodge Royal driven by Elle is actually Tomlin’s own car. “Paul told me he was going to go look at old cars and I mentioned I have one,” Tomlin recalls. “It worked out great and felt comfortable for me because I was experienced behind the wheel.”

Tomlin can speak at length about her admiration for her co-stars, including Laverne Cox and Judy Greer. Garner “looks like an angel” and is a “talent to watch.” Nat Wolff is “a great young actor.” And Sam Elliott, who plays a man from her past, was “a joy to work with.” Tomlin has never worked with the fellow legend before, although Elliott reveals they had met once. “We were both up for a voiceover Emmy,” he says, referring to 2013 when he was nominated for “Robot Chicken” and Tomlin for narrating HBO’s “An Apology to Elephants. “I said hi at the ceremony. Then she beat me.”

That marked Tomlin’s sixth Emmy win in a long and varied career; and this year she finds herself in the running again for her turn on the Netflix series “Grace and Frankie.” The show, currently filming its second season, stars Tomlin and her “9 to 5” co-star Jane Fonda as women whose husbands leave them for each other. Tomlin is having a great time working with Fonda, whom she took with her to Sundance for the “Grandma” premiere.

“It was my first time ever going to the festival,” she reveals. “But Jane had been there several times before. So I let her pick the movies.”

The highlight was the first screening of “Grandma,” where Fonda was sitting in front of her.

“At one point near the end, she just turned to me and gave me a thumbs-up,” Tomlin says. “That was a great feeling and a great review.”

“Grandma” opens this week in limited release.