In a large sauce pan or dutch oven, heat the oil over high heat until almost smoking. Add the popcorn and cover with the lid immediately. Give the pan a shake and wait until you hear the kernels starting to pop. Shake the pan one more time and turn down the heat to medium. Continue to cook until the popping slows down and the kernels are popped, about 2minutes. Pour into a large bowl.
In a small sauté pan, melt the butter over medium heat. Add the lemon zest and cayenne and swirl to let the flavors mingle. Pour the butter mixture over the popcorn and toss gently to coat. Season with salt and serve.