Annoyance Theatre’s “David & David”/Photo: “David & David” team

In writer and director Jake Steelman’s “David & David,” playing now through April 5 at Lakeview’s Annoyance Theatre, David Byrne of Talking Heads fame plays the roommate of Twin Peaks auteur David Lynch in a sitcom-style satire, complete with laugh tracks and a cast of nutty neighbors. The play follows Lynch as he plans a dinner party that will somehow save his ex-girlfriend, Icelandic pop-star Björk, from the clutches of a demon known as the Deerstalker. Meanwhile, sitcom lead Byrne is just trying to celebrate his anniversary with his girlfriend Suzy the Lamp, played by an actual lamp with googly eyes and construction-paper lips.

If that plot synopsis made little sense to you, then we were in the same boat going into Saturday’s debut of “David & David.” I wasn’t sure what to expect from an ensemble cast that features fictionalized versions of Björk, Nicolas Cage, Werner Herzog and Georgia O’Keeffe as the play’s bumbling sitcom neighbors, other than that it was either going to be wildly hilarious or wildly confusing.

Unfortunately, it was mostly the latter.

“David & David” faced an uphill battle bringing to life characters that most people possess only a surface-level understanding of, and some of its actors rose to this occasion better than others. Jordan Baker turned Georgia O’Keeffe into a kooky version of the pigeon lady from “Home Alone,” absolutely stealing every scene she was in. Hobert Thompson’s sardonic, deadpan Werner Herzog was equally hilarious. I was laughing every time they were on stage.

Dane Larson played an angry, and at times almost frightening, Nicolas Cage à la “Moonstruck,” and Katherine Delicath played a name-dropping party-girl version of Björk complete with a stuffed animal swan dress. Both knew their characters well, although Delicath’s Icelandic accent could use some fine tuning. I didn’t know Björk was secretly Russian.

Annoyance Theatre’s “David & David,” with Suzy the Lamp/Photo: “David & David” team

As for the play’s two leads, Jared Narter-Slezak did a fantastic job as a cigarette-smoking, pie-loving, f-bomb-dropping David Lynch, absolutely nailing the director’s unique voice and mannerisms. He also used Lynch’s famously harebrained idioms to hilarious effect. “Faster than a greased-up monkey on a motorcycle” was my favorite.

On the other hand, Calder Amsden’s David Byrne felt a tad stilted, which is to say, he was a convincing Byrne. His recurring scene partner, his girlfriend “Suzy the Lamp,” played by an actual floor lamp, was a reference to the Talking Heads 1984 concert film “Stop Making Sense” in which Byrne dances with a lamp. Aside from a few well-timed lightbulb puns, the bit never quite paid off. It served mostly as a way to give Byrne’s otherwise flat character more dimension than being actually entertaining. I went into my viewing of “David & David” thinking, how do you make David Byrne funny? Unfortunately I’m still asking myself that same question.

“David & David” succeeds at nailing a kookie surrealism that the late David Lynch himself would have appreciated, but at times the play sags under the weight of its own ambitions. I love a high concept—actors playing celebrities who are themselves playing actors in a sitcom—but the play fails to deliver big laughs, more the chuckle of a reference understood than the belly-achers I was hoping for.

“David & David” showing through April 5 at Annoyance Theatre, 851 West Belmont. Showtimes are Saturdays, 10pm. Tickets, $20 plus fees, available at theannoyance.com.