Combine beef, shallot, thyme, Worcestershire, smoked paprika or cumin, and grill seasoning. Combine and divide meat into 4 portions. Form large patties about 1 1/4 inches thick. Coat beef patties with a drizzle of extra-virgin olive oil. Cook 3 to 4 minutes preside for medium rare, 6 to 7 minutes per side for medium well to well doneness.
Cut shrimp along deveining line and "butterfly" them open a little. Be careful not to cut all the way through the shrimp. Leave tails in tact. Place shrimp in a shallow dish. Coat shrimp in extra-virgin olive oil. Sprinkle with grill seasoning or salt and pepper. Add parsley, lemon zest and finely chopped garlic, turn shrimp to coat evenly in flavorings. Wedge lemon which you have zested to pass later at the table with cooked shrimp. Grill shrimp alongside meat patties for 2 to 3 minutes on each side, until heads curl towards tails and shrimp are pink.
While meat and shrimp cook, arrange 4 beds of cut iceberg lettuce on platter and combine horseradish with chili sauce in a small bowl. To serve, place burgers on lettuce "buns" and dot with sauce, then top with 2 grilled shrimp. Pass remaining sauce and lemon wedges at table.