Put oven rack in lower third of oven and preheat oven to 425°F
Toss sweet potatoes with 2 tablespoons oil and 1/4 teaspoon salt in a shallow baking pan. Arrange potatoes in 1 layer and roast, stirring halfway through roasting, until tender, about 25 minutes total. Stir together cayenne, zest, and remaining 1/2 teaspoon salt in a small bowl. Whisk together lime juice and remaining tablespoon oil in a medium bowl, then add potatoes. Sprinkle with cayenne mixture and cilantro, stirring gently to combine.