Combine lime juice and next 5 ingredients in a large heavy-duty, zip-top plastic bag; seal bag, and marinate in refrigerator 30 minutes.
Remove turkey from bag, reserving marinade.
Place marinade in a saucepan. Bring to a boil; remove from heat. Coat grill rack with cooking spray; place turkey on rack over medium-hot coals (350 to 400). Grill, covered, 10 minutes on each side or until turkey is done, turning and basting frequently with reserved marinade.
Cut turkey diagonally across grain into thin (1/4-inch-thick) slices.