‘Imagine my surprise when I found it was possible to be both narrative and anti-narrative at the same time,” Renee Gladman wrote in Calamities, her 2016 collection of meditations on living and writing. She made this discovery during an evening out with friends, but now in My Lesbian Novel she has found a way to express it in a novel as well. This is, as the title promises, a scorching lesbian romance, ending, as the best romances do, in bed, but throughout the book, scenes from the novel alternate with conversations between Gladman and an imaginary interviewer. Curiosity about the novel and curiosity about love wind round each other as she opens up about her structural dilemmas and girds herself to write the next scene.

Gladman is an American author and artist, and sometime architect and mathematician. She writes prose and poetry, fiction and nonfiction; she draws architectural plans and planetary fantasies, and she sees all these not just as connected but as one unified project. She’s drawing lines that may or may not erupt into paragraphs of text, exploring crossings and geographies, mapping the landscapes of our inner and outer worlds. Previously, her fictional urges have found expression in a quartet of novels set in the imaginary world of Ravicka, which comes complete with its own language and is reeling from an ecological crisis that has left buildings disappearing and reforming at will.

The Ravicka novels are full of desire, but the love affairs are distant; one whole book is structured around the intensity of a fleeting encounter on a bridge. Gladman seems to have emerged from them wanting to write a more fully embodied love affair. Indeed, we learn in My Lesbian Novel that during all these years of writing experimental fiction she’s been a connoisseur of popular lesbian romances, with a view to writing her own. The challenge that she sets herself is this: to honour the romance tradition and write a story that will make people “feel good”, while also honouring her commitment to language as a charged, living entity.

The problem with romance, she says in one of the interviews, is that “the genre does not regard language as a living force, as an inhabitable space, a space for encounter”. The problem with literary fiction about lesbians is that it too often ends tragically. “Didn’t we fix this?” she asks herself, reading Naomi Alderman’s Disobedience. “Didn’t we advocate for happy endings for lesbians?”

June, the protagonist, lives with her boyfriend, Ellis. She makes architectural models and is pleased with her life, but there’s a flaw in it: since their trip to London a few months earlier, she has found memories disappearing. “Most of my past acts like it’s covered with fungus, growths that distort details.”

When she meets an English artist, Thena, it becomes clear that this loss of memory began with an encounter between the two women in London that June has entirely erased. She quickly falls for Thena and the promise of consummation is also the promise of revelation: Thena will tell her what happened in London.

Gladman doesn’t like the way romances rely on fake misunderstandings, so she doesn’t put those in their way. There are a few delays and disappearances, and there’s the issue of Ellis (Gladman decides she doesn’t have to write the scenes of June and Ellis growing apart – “I’m not really sure why we’re so in favour of showing over telling”). But then the lovers come together in Thena’s elegant Brooklyn sublet and Gladman writes their love scene with a commitment, tenderness and delicacy that fully meets the challenge she has set herself: this is writing that is at once porous, vital and delightful.

The triumph of this book is to turn our current cultural obsession with all sorts of hybrids and mixtures from an aesthetic challenge into an urgent question of how we can make lives alongside each other. As all the best writers of comedy know, from Shakespeare to Jane Austen, the pleasure of falling in love is a structural pleasure: life at these moments is more narrative than non-narrative. Gladman makes the diagrammatic structure of comedy explicit and in doing so braids together her self-conscious interest in romance fiction as a genre and her growing obsession with it as a source of pleasure.

What next? This is a 140-page book in which the story itself takes up about a third of the pages, so “novel” is a bit of a stretch. The scenes considered but not written do become part of the story, and descriptions of the two women within and outside the narrative amplify each other, with Gladman, who is African American, asking herself whether the two women are going to be Black before she characterises them. But part of the power of this often fascinating book is its longing for a different kind of amplitude altogether. Gladman’s reading of popular romances feels so genuine, the love scene so easy a fusion of readerly and writerly delight, that another kind of novel seems possible – one where the lines erupt not just into paragraphs but chapters.

• My Lesbian Novel by Renee Gladman is published by NYRB (£15.99). To support the Guardian and the Observer, order your copy at guardianbookshop.com. Delivery charges may apply.