I’m not sure what sort of grill you do have, but a basic 22½-inch Weber kettle grill has a tall enough lid to accommodate a beer-can chicken cooked on a typical twelve-ounce beer can. I supposed you could try cooking the bird on a shorter eight-ounce can of beer. Or, the collar that comes with a Weber rotisserie will effectively raise the grill lid by several inches, giving you the clearance you need.