Cut Cornish hens lengthwise through the backbone using kitchen shears, and flatten.
Combine salt and next 4 ingredients; rub evenly over hens. Place hens in 2-qt. zip-top freezer bags or 2 large baking dishes. Whisk together lemon juice and olive oil; drizzle lemon juice mixture over hens. Seal or cover, and chill 1 hour or up to 24 hours. Remove hens from marinade, discarding marinade.
Place hens on cooking grate of grill, and top each with an aluminum foil-wrapped brick. Grill, covered with grill lid, over medium heat (300° to 350°) 18 to 20 minutes on each side, replacing bricks on hens after flipping. Turn grill off, and let stand, covered with grill lid, 5 to 8 minutes or until done. (If using a charcoal grill, transfer hens to a 350° oven, and bake 5 to 8 minutes or until done.) Garnish, if desired.
*Cast-iron skillets may be substituted for foil-wrapped bricks. Place a sheet of foil between each skillet and hen.