To make the salad dressing, whisk together, ketchup, mayonnaise, rice vinegar, lemon zest, lemon juice, chives, and parsley. Season, to taste, with salt and pepper and set aside.
To assemble the carpaccio, place a large tomato slice on each serving plate to be used as the base. Top with 4 thin slices cucumber, distributing evenly atop the tomato. Put a 1/4 teaspoon of salad dressing in the center of cucumbers to anchor a romaine leaf placed curved side up. Top romaine with a small amount of shaved red onion.
Place 1/2 cup of greens alongside carpaccio. Drizzle dressing on and around and serve additional dressing on the side.