MEXICO CITY — Like a lot of good ideas, the concept for LagoAlgo was hatched over a few drinks between friends. In this case, tequila.

Cristobal Riestra, one of Mexico City’s top art dealers, was relaxing with Joaquín Vargas, one of its busiest restaurateurs, at the height of the pandemic shutdown. Mr. Vargas mentioned that he was planning to relaunch a cafe in Chapultepec Park and wanted to make contemporary art part of the mix.

Art is something that Mr. Riestra, the owner of Gallery OMR, a city stalwart for 40 years, knows plenty about.

What started as an invitation to do a temporary pop-up quickly grew into a shared pledge to create a full-blown partnership in what they envisioned as a new kind of attraction, where world-class exhibitions and forward-thinking gastronomy had equal parts, as Mr. Riestra explained. The place would be neither a gallery with a cafe, nor a restaurant that shows art, but rather something in the middle, the whole concept tied together by a shared focus on sustainability.

The anagrammatic moniker came naturally. Lago, which means “lake” in English, was already the name of the restaurant. Algo translates into “something” — a word meant to keep open public perceptions about how the art part could play out.

“We are trying to redefine what an institution like this can be, and how it can function,” said Mr. Riestra, during an interview at the cafe.

LagoAlgo does not just function differently than most food or art establishments, it looks unique, starting with its home, inside a sleek piece of modern architecture that sits on a lake in Chapultepec Park’s second section, a meandering open space with abundant waterfowl and towering Montezuma cypress that is a good half-hour’s hike west of the famous archaeology and art museums in the park’s more manicured first section.

The 1964 structure — designed by the architect Alfonso Ramírez Ponce when he was 23 years old — was part of a citywide redevelopment plan launched ahead of the 1968 Olympics. Mexico City, the proud host, had plans to show itself off as an of-the-moment metropolis and it was deploying the trendy language of modernism to make its case.

Mr. Ramírez clearly understood the strategy, loading the place with the greatest hits of 20th-century design, an open floor plan, concrete walls and floor-to-ceiling windows. He topped the whole thing off with a swooping, saddle-shaped roof — a hyperbolic paraboloid in design-speak — that gave it a distinct presence.

The building has always housed a restaurant in one form or another, starting as a posh supper club where movie stars, like the legendary María Félix, dined and danced while bow-tied waiters pushed around towering dessert carts. Over the decades, though, the eatery had lost its luster, opening and closing while multiple efforts to truly reignite it fell short.

That is, until LagoAlgo came to the rescue. The partners hired the Mexican architecture firm Naso to remake the building, clearing out years of ill-considered renovations, opening up walls and updating furnishings. Mr. Vargas’ CMR restaurant group took inspiration from the natural setting outside to develop a whole new farm-to-table menu. Like everything else about LagoAlgo, the eatery is difficult to categorize. The space has two levels, the lower holding a formal white tablecloth dining room, complete with coat racks and upholstered chairs, the upper looking more like a casual coffee bar and co-working space.

Similarly, the exhibitions do not fall under common art world definitions. Technically, Algo is a commercial gallery — all of the work is for sale, Mr. Riestra reminds visitors — but it has the feel of a nonprofit museum, with group shows by international names.

The current exhibition, “Desert Flood,” co-curated by Jérôme Sans and Mr. Riestra and running through July 31, is a good example. The show has just three artists, but each contributes monumental works, starting with “An Impending Disaster (collaborations)” by the Swiss artist Claudia Comte, a forest of towering marble sculptures, each carved into the shape of a saguaro cactus, and planted on a floor covered in 30 tons of sand imported from a beach in Veracruz. Visitors get sand in their sneakers as they wander through what feels like an indoor desert, admiring art that carries a cautionary message about the state of the environment.

Another gallery space features “We Are All in the Same Boat,” from the Danish art cooperative Superflex. The text-based work is simply the words in its title rendered in blue neon letters, about six feet tall, that are standing on the floor of a dark room. Viewers walk all around the illuminated words, with many of them seizing the opportunity to bask in its moody lighting and snap selfies.

Installed in a nearby foyer is “Wild Quantities” by Gabriel Rico, an artist based in Guadalajara. It consists of a series of 35 neon sculptures, hung from the ceiling, and casting purplish-red hues on the walls, floor and ceiling. The lit-up pieces include numbers and letters, horses and hashtags, and invite viewers to “play with reason and intuition,” according to the exhibition text, as they consider how seemingly unrelated objects can be connected.

The three artists also have other works in the exhibition, and they float throughout the Algo space, which encompasses multiple floors and a variety of rooms large and small. The show’s fluidity mirrors the personality of LagoAlgo overall. Spaces meld together as artworks flow up and down staircases, blend into the cafe area and push outward through the main lobby.

The front yard of LagoAlgo is also part of the building’s lure. The designer Fabien Cappello reimagined it as an energetic public space, with picnic tables and awnings painted in royal blue and school bus yellow, and a food stall serving coffee and beer. People linger for hours, reading books, surfing phones, lounging on hammocks, many without even entering the building. According to Mr. Riestra, nearly 150,000 visitors have come to the site since it opened in February 2022.

Mr. Riestra said the key to success would be keeping LagoAlgo’s different attractions — the art, the food, the historic building — aligned. With their shared focus on sustainability and accessibility, he said, they all “conceptually ask the same sort of questions.”

He wants to keep it open-ended and affordable — admission is free and there is no cost to see the art — with a mixture of unpredictable offerings that keep LagoAlgo’s identity enigmatic.

Mr. Rico, the artist behind the neon sculptures hanging from the ceiling in “Desert Flood,” and who also has a permanent piece in the building’s cafe section, cautions against trying to label LagoAlgo, believing that naming it will limit the possibilities.

“The most dangerous thing is trying to define this as a museum or gallery or a restaurant,” he said. “For me, it is more like a laboratory.”