Lolabelle was a blind, piano-playing rat terrier. The dog was beloved by performance artist Laurie Anderson and her songwriter husband, Lou Reed. You can see the three of them posing for New York Times Magazine, or appearing as a quiet trio in rare TV interviews. In 2011, Lolabelle died. Reed followed two years later, from liver disease.

Last year Anderson released a deeply personal film, Heart of a Dog. From October 20 it’ll have a short run at ACMI in Melbourne.

In a way it’s about the loss of her dog. It’s also about love and empathy, remembering and forgetting, and death.

Watching this film is like floating down a river, staring up at the sky. There’s no plot or predictable path – you’re not sure where you’re being led over its 75 minutes.

Anderson’s voice, inflected with the American Midwest, narrates in a calming, compelling rhythm. A musician and spoken-word artist, she always had a knack for hypnotic pacing (see O Superman, circa 1982).

The film meanders in its curious introspection, from the Tibetan Book of the Dead, to a childhood memory of a hospital stay, but the big and small ideas in it eventually connect. Anderson tells a story, set just after September 11, of taking Lolabelle to a secluded beach and spotting hawks circling overhead. She sees an expression on Lolabelle’s face she recognises from the faces of her New York neighbours. It’s the first realisation of mortality; that, “They could come from the air. I never thought of that.”

Get our pick of the best news, features and events delivered twice a week

While there are unspoken ghosts on the periphery of the film (Reed is never mentioned), Lolabelle is the centre. Anderson imagines what Lolabelle’s doggy view of New York’s West Village looks like. As Lolabelle turns blind in her later years, Anderson brings her a music teacher so she can learn piano. “What kind of music do dogs like?” Anderson wonders.

“Dogs are experts in empathy,” Anderson tells Broadsheet. “They’re so skilled at getting on your wavelength, feeling what you’re feeling. As an artist, I aspire to that.”

As Lolabelle gets sick and old, Anderson decides not to put her down, but to let her face death on her terms.

“Animals are like people,” Anderson says in the film. “They approach death and they back away. It’s a process and you don’t have the right to take that away from them.”

Woven with Anderson’s original and found footage, Heart of a Dog has a texture you want to touch. The images are warped and gently scratched in parts – like an old Super-8 film or a worn photo album. At times it’s blurry – like how a dog sees the world, or the way we recall the past.

Heart of a Dog is not only steeped in memory but in questions about memory – how we remember, and how we shape our own stories by forgetting certain parts of it.

“There are a lot of questions in it,” Anderson says. “I think at the bottom of it is my own question, which is: what is a story, and why do we have them?”

While Anderson is present throughout as a narrator, with the exception of a cartoon rendering at the start she’s never seen on screen. Except for a few haunting seconds.

Partway through Anderson borrows from David Foster Wallace: “Every love story is a ghost story”. The camera swings carelessly sideways, pointing at a sandy beach. It then pans upwards, showing Anderson’s face against a vast sky. It falls on an angle again, and there’s Reed sitting on the sand with his pants rolled up and hair windswept, watching her from beyond her reach.

Heart of a Dog shows at ACMI from October 20 to November 6. Tickets and full program available here.