Last year, Coach, the handbag and accessories company, hired Lite Brite Neon Studio to create a six-foot-tall pink Tyrannosaurus Rex for its store in the SoHo neighborhood of Manhattan.

But when Matt Dilling, Lite Brite’s founder, saw the sketches for “Rexy,” as the dinosaur is known, he was shocked. “It was like a drug-induced hallucination,” he said. “And I mean that with the utmost respect.”

Mr. Dilling, 38, has run Lite Brite for almost 20 years. In the past, he said, clients merely wanted to light up their logos. To him, this wasn’t just boring; it lacked appreciation for the medium’s creative potential.