The Lonely Few is the name of the band that jams at Paul’s Juke Joint. Front woman Lila (Lauren Patten), who by day works as a clerk at the local Save-A-Lot, is too talented to be trapped in this backwater. But she feels unable to leave her older brother, Adam (Joshua Close), an amiable duffer with a substance abuse problem.

Lila and Adam have looked after each other ever since their mother died. Lila has big dreams for herself, but she values loyalty more than success. To stay sane, she releases her pent-up frustration at her gigs, where her furious guitar playing, powerful vocals and introspective songwriting torch the everyday drabness of her life with a Dionysian flame.

On one of these occasions, a special guest appears at the bar. Amy (Ciara Renée), a Black singer-songwriter who is testing the waters of a solo career, turns up one night at the invitation of Paul (Thomas Silcott), her former stepfather, who’s not only the proprietor but also the Lonely Few’s drummer. Amy recognizes right away that Lila is no ordinary singer. She also sees that they have something else in common as lesbian rockers in the intolerant South.

A love story comes into meteoric focus in this musical, which features a book by Rachel Bonds and a score by Zoe Sarnak. Two women who are attached to their cultural roots yet alienated by the conservative values of their communities hold for each other the answer to problems that until now have seemed insuperable.

Lila, longing for freedom, is in need of a way out. Amy, hungry for belonging, is in need of a way in. But the course of true love never did run smooth, as Shakespeare memorably put it. And the marginalization of being queer will only compound the obstacles to a possible happy ending for these characters.

Stage actors are often called upon to play famous rock stars in jukebox musicals, which rely on an audience’s affection for popular music catalogs. “The Lonely Few” makes its cast members earn their rock-and-roll stripes.

There’s no cover band medley of old hits to win over restless audience members, so the performers have to cast their own incandescent spell when jamming. The production — fluidly directed by Trip Cullman and Ellenore Scott on a set by Sibyl Wickersheimer that makes imaginative use of unsuspecting corners of the Geffen Playhouse’s second stage — is fortunate to have two gifted singers leading the charge.

Patten won a Tony Award for her featured performance in “Jagged Little Pill,” the Alanis Morissette and Diablo Cody musical in which she delivered a version of “You Oughta Know” that regularly brought the house down. (The role was the subject of some controversy related to the production’s handling of the gender identity of Patten’s character.) Lila’s musical style is eclectic, blending the mercurial emotionalism of Morissette’s music with Melissa Etheridge’s classic rock authority. Patten makes Broadway virtuosity perfectly compatible with roadhouse authenticity.

Renée has astonishing vocal agility that can sweep into the upper range from the lower depths. Her singing is almost too good, but then she’s playing a noted recording artist whose stardom would be greater if it weren’t for society’s close-mindedness. She endows Amy with the melancholy radiance of an artist who’s struggling to clear an independent path.

Ciara Renée and Thomas Silcott in “The Lonely Few” at Geffen Playhouse.

(Jeff Lorch / Geffen Playhouse)

The entire cast is terrific, with each role etched with enticing idiosyncrasy. As Adam, Close honors the disarming generosity that makes it so hard for Lila to abandon her brother. Silcott’s Paul shows himself to be a man who wants to rectify his past lapses, and this integrity comes to the fore as Paul and Amy dig into the complications of their history.

Helen J Shen plays JJ, the precocious 17-year-old keyboardist in the Lonely Few, in a way that accentuates the character’s wacky ambition without losing sight of the youngster’s preternatural sensitivity. In the role of Dylan, a bandmate, buddy and booster of Lila’s, Damon Daunno (a Tony nominee for his performance as Curly in Daniel Fish’s revival of “Oklahoma!”) creates a dorky charmer eager to hitch a ride to the big time even as he knows he’ll have to get off soon and face his responsibilities at home.

The galvanizing singing, inventive staging and charming acting can’t entirely cover up the musical’s chief problem — choppy storytelling. It might be tempting to place the blame on Bonds’ book, which has some cliched dialogue, predictable plot points and familiar confrontation scenes. Weirdly, for a modern musical about a lesbian couple, the writing harks back to the sentimental tactics of an earlier, more conventional era. (Playwright William Inge’s characters, desperate to find connection in unfavorable provincial circumstances, have a surprising amount in common with “The Lonely Few” gang.)

Lauren Patten and Joshua Close play siblings in “The Lonely Few,” directed by Trip Cullman and Ellenore Scott.

(Jeff Lorch / Geffen Playhouse)

But the fault doesn’t lie solely with the book. It’s the relationship between the drama and the music that’s off-kilter.

Sarnak’s lyrics are often drowned out in the production’s sound volume, frustrating those who expect the songs of a musical to advance the story. But not all of the audible lyrics shed meaningful light on the characters, and a few create leaps in the action that don’t seem fully earned.

The show’s rhythm, as a result, is derailed. The songs grow in lyrical interest in the second act, but the storytelling drags, especially in the prolonged final stretch. “Wondering” beautifully exposes Amy’s vulnerability and “Always Wait for You” movingly expresses Lila’s romantic realization, but the psychological context and theatrical deployment of these numbers could use some tinkering.

“The Lonely Few” cries out for clarity and compression. But it’s an endearing new musical with some untapped potential. Love stories, even queer ones, can’t help being a little old-fashioned at their core. But this one still has more originality to discover.