Cut backbone from chicken using kitchen scissors and save backbone for another use, such as stock. Flip chicken, breast-side up, and forcefully press chicken down to flatten; season generously with salt.
Heat olive oil in a large oven-safe, heavy-based pan over medium-high heat; pan-fry chicken, skin-side down, until golden, 6 to 7 minutes. Transfer chicken to a plate, skin-side up.
Cook and stir onion in oil in the same pan until softened, 2 to 3 minutes. Add beer, scraping up any browned bits from the bottom of the pan. Continue cooking until most of the beer is reduced, 2 to 4 minutes more. Stir chicken stock, carrots, lemon, rosemary and thyme into beer mixture. Arrange chicken, skin-side up, over vegetables.
Roast in the preheated oven until chicken is golden brown and juices run clear, about 50 minutes. Transfer chicken and vegetables to a large platter and let rest, uncovered.
Bring remaining stock and juices in the pan to the boil and cook until sauce is thickened, about 10 minutes. Season sauce with salt.