Make the glaze: Combine the honey, Worcestershire sauce, lemon zest, lemon juice, thyme, 4 ounces of the malt beverage, a pinch of salt and way more pepper than normal in a saucepan on medium heat. Cook until slightly reduced and glaze-worthy, about 5 minutes.
Prepare the chicken: Pat the chicken dry all around, then pat it dry again. Rub with the oil all over and sprinkle with salt and pepper. Place the chicken over the can, through the back end with the neck up. Place in a small pan.
Grill and glaze the chicken. Heat a grill for cooking with indirect heat to 325 degrees F.
Place the pan over the side of the grill with indirect heat and cook, brushing the chicken with the glaze every 20 minutes, until the internal temperature is around 155 degrees F, about 1 hour, 15 minutes. Remove and slightly tent with aluminum foil to rest and let the temperature rise to 165 degrees F, about 15 minutes. Carve and serve.