1. Preheat grill to high (if using a charcoal grill, the coals are ready when you can hold your hand 5 inches above grill for just 2 seconds). Brush 2 large fish-grilling baskets with oil. Using a sharp knife, make diagonal slits (in serving-size portions) along both sides of fish. Season both sides with salt and pepper. Reserve 6 to 8 lemon rounds and a few sprigs of thyme; place remaining lemon rounds and thyme inside fish cavities.

2. On a large cutting board, lay 2 bacon slices end to end, slightly overlapping; repeat with 6 more slices, laying pairs parallel to one another, 1 inch apart. Center 1 bacon slice at top and bottom, 1 inch apart from and parallel to overlapping slices. Lay fish over bacon, placing head and tail on single slices. Wrap fish in bacon, and secure with toothpicks. Tuck a few reserved thyme sprigs under bacon. Place fish in basket. Repeat with remaining fish, bacon, and thyme.

3. Grill fish, covered, turning once, until opaque throughout, about 10 minutes per side. Transfer to a platter. Grill reserved lemon rounds until lightly charred. Garnish fish with thyme, grilled lemon slices, and lemon pieces.