Whisk together lemon juice, salt and pepper, then slowly add olive oil in a stream, whisking until combined. Add oregano and set aside.
Along the middle of each fish make 1-inch long diagonal slashes at 2-inch intervals on both sides of the fish. Brush fish all over with vegetable oil and season with 1 teaspoon each of salt and pepper (total).
Season the fish cavity with salt and pepper. Insert 2 lemon slices and 2 sprigs of oregano in each fish. Using kitchen string tie fish closed at 2-inch intervals.
Oil grill rack then place branzino on the grill. Close lid and cook for 6 minutes. Turn fish over using 2 metal spatulas. Cook for another 6 minutes or until cooked through.
Transfer fish to platter, remove string and garnish with more lemon. I say let each guest cut off the head and remove the bones of their own fish.
Serve fish with vinaigrette dressing.
Vinaigrette Dressing
Combine garlic, red wine vinegar, olive oil, salt & pepper in a jar and shake. Set aside a third of the vinaigrette to serve with the fish at the table. Use the remaining vinaigrette to brush the vegetables.
Ratatouille
Red Onion: Cut the ends off of each onion and peel. Holding the flat sides of the onion with your hand push skewers into the onion imagining where you will cut it to make 4 thick slices. The skewer should go through the onion right to the cutting board. Now insert a second skewer into each slice at a different angle. Cut the onion into thick slices cutting between the skewers. Push the skewers further through the onion to hold the slices together. Brush with vinaigrette and grill until soft, 8-10 minutes, turning once. Remove skewers and chop coarsely.
Peppers: Brush peppers with oil and grill until skin is blackened, about 10 minutes. Place in a plastic bag for 5 minutes. Peel peppers, remove stem and seeds, cut into strips.
Squash and Eggplant: Brush with vinaigrette and grill until soft, about 5 minutes, turning to cook all sides. Chop into bite size piece.
Tomatoes: Brush with vinaigrette and grill until soft, 3-5 minutes, turning once. Chop coarsely.
Final Assembly: Combine all grilled vegetables in a bowl, add parsley and basil. Toss with remaining vinaigrette. Serve with grilled fish.
Notes
Grilling can be part of the entertainment depending how big the crowd is. The grilled ratatouille can be prepared a few hours in advance if you prefer fewer last minute tasks.