1If using charcoal grill, place drip pan directly under grilling area, and arrange coals around edge of firebox. Heat coals or gas grill for indirect heat. Loosen skin on turkey in 4 or 5 places. Carefully place lemon slices and basil leaves under skin. Rub turkey skin with oil; sprinkle with lemon-pepper seasoning. Insert barbecue meat thermometer so tip is in thickest part of turkey.
2Cover and grill turkey, skin side down, over drip pan or over unheated side of gas grill and 4 to 6 inches from medium heat 20 minutes; turn. Cover and grill 35 to 45 minutes longer or until thermometer reads 170°F and juice of turkey is clear when center is cut.
3Remove turkey from grill; cover with foil tent and let stand 10 minutes. Slice turkey.