Alana Haim and Cooper Hoffman in Licorice Pizza (Paul Thomas Anderson/MGM)

Lucille Ball is everywhere these days. She’s a subject of Aaron Sorkin’s upcoming Being the Ricardos; she receives the biography treatment from the Turner Classic Movies podcast, The Plot Thickens; and she even pops up in Paul Thomas Anderson’s latest Los Angeles-based opus, with Christine Ebersole as her fictional counterpart, Lucille Doolittle.  

The comedian is one part of Anderson’s gumbo. Sean Penn appears as a movie star with the DNA of William Holden, and the story line is ripe with references to the pop culture of the early 1970s: Deep Throat, Live and Let Die, and Yours, Mine and Ours (a 1968 Ball vehicle), here called Under One Roof. The writer/director has also made perhaps the first comic set piece centered around the energy crisis of 1973. The soundtrack doesn’t pick a lane either, jumping among Bing Crosby, Sonny and Cher, David Bowie and Taj Mahal.

At an Encino high school, a cocky 15-year-old Gary Valentine (Cooper Hoffman, in his first film) has the tenacity to ask an older woman on a date. She’s 25—but later at one point, she lets slip she’s 28—and works for the photographer taking yearbook photos. Gary promises Alana Kane (Alana Haim) that he will sweep her off her feet. As proof that he’s not just a pimply-faced kid, he boasts about his most noted acting credit, a hit family friendly film. (And yes, Anderson has said that he wrote the role of Alana with Haim in mind; he has directed several music videos of the all-sisters pop rock band Haim. She makes up one-third of the group.)

Alana goes on the date more out of curiosity, and perhaps because she has nothing else to do, that evening at the hot spot Tail o’ the Cock, which was an actual San Fernando Valley restaurant. (They drink cokes, no rum.) At the end of the night, she shuts down the possibility of seeing him again, but when opportunity calls, she can’t resist posing as Gary’s chaperone for an East Coast TV appearance promoting his hit film. However, any fantasies Gary may have about a New York rendezvous are popped when she begins dating his older costar, Lance (Skyler Gisondo), handsome and ostensibly Jewish, a suitable young man to take home to her parents. But time and again, when she has a pie-in-the face moment, Alana comes back and joins forces with Gary on his schemes. At least with the honest and direct teen, she knows what to expect.

It’s not as though Gary comes across as older than his years. Instead, he will grab at one idea one week and then jump on board with another the next, knowing that he has aged out of roles and doesn’t have the talent to continue an acting career. Somehow, he sets up a store and has some sort of agreement with a manufacturer to sell waterbeds. Later, he’ll bring pinball machines back to Los Angeles.  

Both leads have an easy rapport, and the film coasts along largely on their charms. Hiam especially makes a confident, spirited film debut. As Gary and Alana hop from romp to romp, she regresses in age, becoming jealous of a 15-year-old girl and intentionally making Gary upset when she goes out with a major movie star—perhaps that explains her baby doll dresses. Yet the screenplay refrains from making any point or statement about this May-December pairing between an aging child actor and a woman who still lives at home with her parents, and isn’t going to school or dating. She’s a slacker two decades ahead of her time. Like much of the movie, the central premise asks to be taken at face value. (If the genders were reversed, the scenario would be downright creepy and the film would never have been made, at least not with this budget.)  

It’s obvious what Gary sees in Alana, especially in a shot from his perspective of her midriff, as they lie next to each. But for Alana, the various escapades she shares with Gary and his mates perhaps give her a sense of control. She’s certainly the center of attention with these teenage boys, and she’s literally in the driver’s seat, at the helm of a huge moving van fleeing from an unhinged Jon Peters. (Yes, the same Peters who was Barbra Streisand’s boyfriend around this time.) Though Alana is self-possessed and articulate, she may not be as smart as she thinks she is. When she’s asked out by big-time movie star Jack Holden (Penn), he takes her to the Tail o’ the Cock. Maybe it’s because she’s having her first martini ever, but she can’t look past the praises the smooth talker piles on her to see them for what they are: come-ons he has used on countless young women.

Just like Gary and Alana, Anderson’s winging it too, considering the 133-minute running time. The screenplay makes up their adventures as it goes along, to the extent that some of the sequences are overstretched, like the one with a ranting and raving Jon Peters. As a series of episodes, the movie entertains more than it drags, though it’s loosely hung together.

However, Anderson smartly surrounds his two newbie leads with some of the best character actors around. He was wise not to cut from the close-up of Harriet Sansom Harris as a Hollywood agent giving Alana the rundown of how she would position the wannabe actress in Hollywood. As a compliment, she sees Alana as a tenacious “English bulldog with a Jewish nose.” Tom Waits staggers in as a Hollywood insider, and Bradley Cooper nearly disappears under the sunglasses and big-hair wig as Peters. Maya Rudolph steals her one scene with just a raised eyebrow, and the Lucy Doolittle episode offers the biggest laugh. Watch for a certain reaction from Ebersole.