Pat the birds dry, inside and out, with paper towels. Trim any extra skin around the cavity of the duck. Running your hands beneath the skin, carefully separate the skin from the flesh without tearing or removing it. Season the outer part of the skin and the inner cavity of both birds generously with salt and pepper, then transfer to the refrigerator and let rest uncovered at least 6 hours or overnight.
In a hearth or fire pit, prepare a small fire. Alternatively, set a rack in the center of an indoor oven and preheat to 350°. In a small pot, warm the lard or other fat and add the armagnac, thyme, and garlic. Brush both birds with the lard mixture. Using a 3-foot piece of twine soaked in water, hang the duck by the limbs or cavity above the fire; or in a large roasting pan fitted with a rack, position the duck off to one side of the rack. If hanging the bird, set a pan beneath it to catch any drippings.
Roast the duck until the skin is just starting to color and some of the fat has rendered, about 25 minutes.
If cooking with fire, move the duck closer to the heat source, or add more wood to the fire as needed to increase the heat. If cooking in a home oven, retrieve the roasting pan and raise the oven heat to 525°. Meanwhile, baste the duck with some of the rendered fat from the pan, or more of the rendered lard mixture. Hang the pheasant next to the duck, placing a pan beneath it to catch drippings, or adding it to the other half of the roasting pan.
Roast both birds until the skin is browned and the juices from the leg joints run mostly clear when poked with a paring knife, about 25 minutes. Remove the birds briefly and brush with the warmed jelly. Roast, swiveling the birds on strings or rotating them as needed, until the skin is caramelized and darkened, 5–10 minutes more (watch closely for burning).
Remove and let the birds rest 5 minutes. before carving. Serve the pieces in a shallow pool of the pan drippings.