In a large saucepan or Dutch oven, heat the oil over medium-high heat until nearly smoking. Add the popcorn kernels and immediately cover with a lid. Give the pan a shake and wait until you hear the kernels starting to pop. Shake the pan again, then lower the heat to medium and continue cooking until the popping slows and the kernels are popped, about 2 minutes more. Transfer the popcorn to a large bowl.
Melt the butter over medium heat in a small saute pan. Add the lemon zest, cayenne and 1/2 teaspoon salt. Swirl to mingle the flavors. Pour the butter mixture over the popcorn and toss gently to coat. Season with salt and serve.