Whisk together the lemon juice, Worcestershire and steak sauce in a small bowl. Place the chickens in a large baking dish and rub with the butter then pour the lemon mixture over. Cover and place in the refrigerator for at least 2 hours and up to 4 hours.
Preheat the grill to medium.
Season the chickens liberally with salt and pepper and place on the grill, skin side down. Grill until golden brown and slightly charred, 10 to 12 minutes. Turn over, close the cover and continue grilling until an instant-read thermometer inserted into the thigh registers 165 degrees F. Remove, tent with foil and let rest 10 minutes before carving.