1. At the meat market, have turkey backbone sawed through lengthwise. Or at home, use spring-loaded poultry shears to cut through length of backbone. Lay turkey on its breast; pull open from back, pressing to flatten (some bones will crack). Pull off and discard lumps of fat.
2. Rinse turkey and pat dry with towels. Squeeze and rub 1 or 2 lime halves over turkey; sprinkle with oregano, then season lightly with salt and pepper.
3. To barbecue with charcoal, use a barbecue (20 to 22 in. wide) with a lid. Mound and ignite 40 charcoal briquets on firegrate. When coals are spotted with gray ash, in about 20 minutes, push equal portions to opposite sides of firegrate. Place a foil or metal drip pan between coals. To each mound of coals, add 5 briquets now and every 30 minutes while cooking.
To barbecue with gas, use a barbecue with indirect heat controls at least 11 in. between burners. Turn all burners to high, close lid, and heat for about 10 minutes. Adjust gas for indirect cooking (heat parallel to sides of bird and not beneath) and set a foil or metal drip pan in center (not over direct heat; if drippings flare when lid is open, add a little water to pan).
Set grill in place. Lay bird, bones down, on grill over drip pan.
4. Cook turkey until thermometer registers 160° at thickest part of breast at bone, about 1 1/2 hours. Start checking at 1 hour.
5. Transfer turkey to a large platter. Keep warm and let stand 15 to 30 minutes, then carve. Accompany with remaining limes to add juice to taste.
Nutritional analysis per 1/4 pound boned cooked turkey with skin, based on percentages of white and dark meat in an average bird.