Place a rimmed baking sheet in the oven and preheat to 425 degrees F. Cover the red onion with cold water in a small bowl and set aside. Toss the sweet potatoes with 2 tablespoons olive oil, the curry powder, 1/2 teaspoon salt and a few grinds of pepper in a large bowl. Spread the sweet potatoes in a single layer on the hot baking sheet and roast until tender and browned around the edges, 20 to 25 minutes.
Meanwhile, whisk the lime zest and juice, mango chutney, remaining 3 tablespoons olive oil, 1/4 teaspoon salt and a few grinds of pepper in a large bowl. Drain the red onion and add to the bowl along with the kale, lettuce, chicken and half the herbs; toss to coat. Season with salt and pepper. Divide among bowls and top with the sweet potatoes, cashews and remaining herbs.