Finely shred peel and squeeze juice from half of the lemon; thinly slice the remaining lemon half and set aside. In a small bowl combine mayonnaise, lemon peel, lemon juice, basil, salt, and pepper.
Rinse fish; pat dry. Remove 2 tablespoons of the mayonnaise mixture and brush onto fish. Place fish, skin side up, on the rack of an uncovered grill directly over medium-high heat; grill for 1 minute. Carefully turn skin side down and grill 5 to 7 minutes more or just until fish flakes easily with a fork. Add lemon slices and halved buns, cut side down, to the grill after turning fish.
Remove fish, buns, and lemon slices from grill. If desired, remove skin from fish. Cut fish into bun-size pieces. Top bun bottoms with some of the mayonnaise mixture. Add fish, lemon slices, and, if desired, additional basil. Pass any remaining mayonnaise mixture.