Heat 1 tablespoon oil with 3 popcorn kernels in a large, heavy saucepan over medium heat. When kernels pop, add remaining 1/2 cup kernels. Cook, covered, shaking pan occasionally, until popping slows, 6 to 7 minutes. Remove pan from heat; let stand, covered, 1 minute.
Stir together spices, salt, and zest in a small bowl. Toss hot popcorn with remaining tablespoon oil in a large bowl; sprinkle with spice mixture. Squeeze lime wedge over popcorn. Toss to coat.