A North Carolina maker of lighting products tried to convince the Trump administration that paying tariffs on its goods coming out of China would threaten its spending on research and jobs in the U.S.

It didn’t work. Cree Inc., already contending with low-cost competitors in its light-emitting diode business, will face a 25% duty this week on LEDs shipped to the U.S. from its plant in China—costs the company said will wreak upon it “disproportionate economic harm.”

Cree’s...