Preheat grill to high. Preheat oven to 350°. Toast cornbread 10 minutes. Whisk together 2 tablespoons juice, 2 tablespoons olive oil, and 1 1/2 teaspoons cumin. Brush 1 tablespoon mixture on chicken; season with salt and pepper. Grill 5 minutes per side; slice. Toss cornbread, 1 1/2 cups tomato, 3/4 cup onion, and romaine with dressing. Season with salt and pepper. Top with chicken.