Preheat the oven to 425 degrees F (220 degrees C).
Rub each hen with a lime half. Drizzle with olive oil, then season with chili powder, cumin, kosher salt, and black pepper. Place hens on a rack in a shallow roasting pan.
Roast hens in the preheated oven for 15 minutes.
Reduce oven temperature to 350 degrees F (175 degrees C).
Continue roasting until no longer pink at the bone and the juices run clear, about 30 minutes. An instant-read thermometer inserted into the thickest part of the thigh, near the bone, should read 165 degrees F (74 degrees C). Remove from the oven, cover with a doubled sheet of aluminum foil, and allow to rest in a warm area for 10 minutes before slicing.