Thaw Cornish game hens, if frozen. Finely shred enough lemon peel from 1 of the lemons to make 2 teaspoons peel. In a small bowl combine herbs, salt, pepper, and lemon peel; set aside. Cut one and a half of the lemons into slices; cut remaining lemon half into four wedges.
To prepare Cornish hens, remove giblets, if present. If desired, remove skin from hens. Rinse hens; pat dry. Place hens on a plate or baking dish. Place 1 lemon quarter in each hen cavity. (If using chicken breasts, omit lemon quarters.) Tie drum sticks to tail using heavy kitchen string. Twist wing tips under the back. Generously pat outside of birds with herb mixture. Lay lemon slices over top. Wrap tightly with plastic wrap and chill in the refrigerator for 12 to 24 hours.
For a charcoal grill, arrange medium-hot coals around a drip pan. Test for medium heat above the pan. Place Cornish hens (breast side up) on grill rack over drip pan. (Place breasts, bone side down over drip pan.) Cover and grill for 50 to 60 minutes or until meat is tender, no longer pink, and instant-read thermometer inserted into thigh muscle registers 180 degree F. (For a gas grill, preheat grill. Reduce heat to medium. Adjust for indirect cooking. Grill as above.)
Remove hens from grill. Cover with foil and let stand 10 minutes before carving. Makes 4 servings.