Preheat oven to 450 degrees F.
Rinse hen and pat dry. Remove liver and giblets and set aside. Place sprig of thyme and 1/2 lemon in cavity of bird, rub bird with 2 tablespoons olive oil, season inside and out with salt and pepper and place on roasting rack in roasting pan in oven. Cook for 50 minutes or until juices run clear from knife cut at thigh joint.
To prepare sauce, heat 4 tablespoons olive oil in a 12 to 14 inch saute pan over medium heat. Add onion, garlic and sausage and cook until soft but not brown. Add 2 tablespoons water, if it starts to brown. Add sage, guinea hen giblets, and liver and chicken liver and continue cooking slowly for 8 to 10 minutes, or until everything is soft and gray. Add orange zest and juice, vinegar, sugar, cinnamon, chili flakes and black pepper and simmer five more minutes, mashing with a potato masher to form a fine paste. Remove guinea hen when cooked, let rest 5 minutes, carve and bring to table. Place peverada in a bowl and serve on the side.
Recipe Courtesy of Mario Batali