Heat the oven to 450 degrees F. Toss the carrots with 1 tablespoon of oil on a baking sheet. Season with salt and pepper, then arrange cut-side down. On a second baking sheet, toss the sweet potatoes with 1 tablespoon of oil. Season with salt and pepper, then arrange cut-side down. Roast for 15 minutes, then flip the vegetables, add the cranberries to either sheet, and roast until tender, 5 to 10 minutes more.
Meanwhile, in a small bowl, stir together the lime juice and zest and 2 tablespoons oil. Season to taste with salt and pepper, then stir in the chili.
Transfer the carrots, sweet potatoes, and cranberries to a serving platter (or combine everything on one baking sheet). Drizzle with dressing and season with salt and pepper as desired.