Prepare the dressing by mixing mayonnaise, ketchup, lemon juice, red apple vinegar, Worcestershire sauce, and sweet pickle relish in a bowl. Whisk until smooth and chill in the refrigerator.
On a large platter or individual plates, create a bed of chopped romaine lettuce. Layer with shrimp, sliced hard-boiled eggs, halved tomatoes, avocado slices, cucumber, red onion, and black olives if using.
Drizzle the chilled dressing over the salad or serve it on the side. Garnish with lemon wedges for an extra touch.