Amy Lau, a New York interior designer and a founder of the annual Design Miami fair, whose vernacular was the saturated colors of the American Southwest and whose deep knowledge of modernist objects was the foundation of her work, died on Jan. 17 in Scottsdale, Ariz. She was 56.

The cause was cancer, her family said.

Ms. Lau’s success did not rest on an ability to parse paint colors and match furniture and rugs (although of course she could do both things). Rather, it was her consummate talent for choosing important pieces — for example, a sofa designed by Vladimir Kagan, a sculpture by Anish Kapoor, a bronze work by the furniture sculptor Silas Seandel — and crafting warm, striking interiors around them. Those selections were the raison d’être, not the afterthought.

“Designers all begin from some vantage point, and Amy’s was her knowledge of midcentury modern,” Amanda Nisbet, an interior designer in New York and Palm Beach, said in an interview. “But she was also a real supporter of current artists and artisans, and sought out the work of the ones she thought were worthy of her clients’ money.”

Those clients included the media executive and Seagram heir Edgar Bronfman Jr. and his wife, Clarissa; the fashion designer Elie Tahari (Ms. Lau designed his East Hampton boutique); and the real estate developer Craig Robins.

It was Mr. Robins with whom Ms. Lau teamed up in 2005, along with the designer Ambra Medda, to start Design Miami, a collectible-design fair conceived to run in tandem with the annual art fair Art Basel Miami Beach. It has become an important showcase and destination for designers and their clients.

“Amy was the first of a new generation of designers entering the industry at the end of the 20th century,” the New York interior designer Vicente Wolf said in an interview. “She was unrestrained in the sense that she wasn’t going to do things the way everyone else was doing things — in her mixture of furniture and her use of color.”

He added, “She was a firecracker, with the hair color to go with it.”

Mr. Wolf wasn’t the only colleague to mention Ms. Lau’s striking red hair — a shade that, coincidentally, often turned up in her interiors.

As Ms. Nisbet put it, “Amy embodied her design aesthetic.”

Amy Marie Lau was born on Dec. 12, 1968, in Scottsdale, Ariz., the eldest of four children, and was raised in nearby Paradise Valley. Her father, Frederick Lau, a dentist, and her mother, Patti (Cochran) Lau, who managed the household, were avid collectors of Southwestern art and artifacts; her paternal grandmother, Ruth Lau, was a painter of Arizona desert scenes. Another relative was a founder of the Taos School, an early-20th-century art movement whose palette — the blues of skies; the yellows, corals, apricots, tans and, yes, reds of the Southwestern landscape — would inform Ms. Lau’s interiors.

“I still think of its dusty olives, siennas and rusty brown as ‘my colors,’” she wrote in her first monograph, “Expressive Modern” (2011).

After receiving a bachelor’s degree in art history from the University of Arizona in 1992 and a master’s in fine and decorative arts from the Sotheby’s Institute of Art in Manhattan in 1995, Ms. Lau became the manager of Aero, the New York design gallery and boutique. She later became the design director of the Lin-Weinberg Gallery in SoHo, now Weinberg Modern, which specialized in international midcentury-modern design.

“Amy’s aesthetic vision took shape at our gallery,” said Larry Weinberg, one of its owners. “The roomlike vignettes, window displays, the selection of fabrics for upholstered pieces — these were all core skills for an interior designer, and all things Amy excelled at.”

In 2001, Ms. Lau founded Amy Lau Design, where she made it her brief to create residential and commercial spaces that filtered various styles, objects and client preferences through the lens of modernism. In the years that followed, she began designing products for Heath Ceramics; Kohler; S. Harris, a supplier of high-end fabrics; and Maya Romanoff, a manufacturer of handmade wall coverings.

This past fall, Ms. Lau opened a gallery in the New York Design Center — “a longtime dream,” said Sharon Bray, the business manager of Amy Lau Design. Contemporary and vintage glass, ceramics and metalwork share space there with textiles and furniture.

Ms. Lau is survived by her parents and her siblings, Megan Hackbarth, Kati Travelle and Matthew Lau.

Ms. Lau, a perennial renter, bought a one-bedroom apartment in Alwyn Court, a prewar building in Midtown West, in 2018 and spent the next six years renovating — a daunting project, as the home hadn’t been updated since the 1980s. She moved in once the major construction was completed, while the rest of the work continued around her.

Ms. Lau, who called the apartment her sanctuary, “put together a lot of contemporary and vintage pieces that she loved from artists and artisans that she loved,” Ms. Bray said of a group that included Mr. Kagan; Michael Coffey, a woodworker; and Erik Bruce, a designer and manufacturer of window treatments. Ms. Lau herself designed the wallpaper for the bedroom and the foyer. An Art Nouveau Jugendstil chandelier that she found in Europe was the focal point of the home. (On Saturday, Architectural Digest posted a feature about the apartment.)

“When the window treatments were finally installed this past September — which meant that all the work was done — Amy was overjoyed,” Ms. Bray said.

As a client, her boss “was detail-oriented and exacting,” she added. “She knew what she wanted.”