1. Preheat grill to medium heat (300°F to 350°F). Toss zucchini, bell peppers, onion and Italian seasoning with 2 Tbsp. olive oil in a large bowl or roasting pan. Grill vegetables, covered, until just tender but still crisp, 4 to 6 minutes on each side. Transfer vegetables to a cutting board and chop into bite-size pieces. Whisk balsamic vinegar, 1 tsp. lemon juice, remaining 1 Tbsp. olive oil and 1 tsp. each salt and pepper in a large bowl; add vegetables and toss. Cover and let stand.
2. Whisk cheese with mayonnaise, lemon zest and 3 Tbsp. juice. Sprinkle fish with salt and pepper and brush with cheese mixture. Brush grill grates with oil. Grill fish, covered, until cooked through, 3 to 4 minutes per side for fillets or 6 to 8 minutes per side for steaks. Serve with vegetable mixture.