Rinse the chickens and pat dry. Heat oven to 375° F.
Place the lemon and garlic in the chickens' cavities. Tie the legs together. Rub the birds with some oil, then sprinkle with the salt and lots of pepper. Tuck some thyme sprigs between the breasts and the thighs and wings. Put the remaining sprigs in the roasting pan and place the chickens on top. Roast for 1 1/2 hours or until an instant-read thermometer inserted in the thickest part of a thigh reads 180° F. Remove the chickens to a platter. Pour any juices that accumulate back into the pan. Discard the thyme. Place the pan over medium heat, add the wine, and bring to a boil, scraping up any brown bits from the bottom.
Pour the pan juices into a cup and place in the freezer for about 10 minutes to hasten the separation of the fat. Discard the fat and heat the remaining juices in a saucepan or in the microwave. Serve with one of the chickens. Wrap and refrigerate the other chicken for another meal.