Roast Chicken with Pan Gravy

Preheat oven to 450°F with rack in middle.
Pull off excess fat around cavities of chickens and discard, then rinse chickens and pat dry. Melt 4 tablespoons butter with garlic and brush butter all over chickens. Season both chickens inside and out with 2 1/2 teaspoons salt and 1 teaspoon pepper (total). Put half of garlic and 1 lemon half in each cavity and loosely tie legs together with string.
Roast chickens in a large (17-by 11-inch) flameproof roasting pan, basting with pan juices using a spoon (remove pan from oven and tilt if necessary) every 20 minutes, rotating pan, until an instant-read thermometer inserted into fleshy part of a thigh of each chicken (do not touch bone) registers 170°F, 50 to 60 minutes total. Baste chickens once more, then carefully tilt them so juices from cavities run into roasting pan. Transfer chickens to a cutting board (reserve pan) and let rest 15 minutes before carving.
Pour off all but 2 tablespoons fat from pan, then cook remaining drippings over medium-high heat until deep golden, 1 to 2 minutes. Add flour and cook, stirring constantly, 1 minute. Stir in water and simmer, stirring and scraping up brown bits, until thickened, about 3 to 4 minutes. Whisk in remaining 4 tablespoons butter and lemon juice to taste (from remaining lemon halves). Season with salt and pepper. Strain through a fine-mesh sieve into a gravy boat.