For the cocktail sauce: In a small mixing bowl, combine the ketchup, horseradish, lemon juice, Worcestershire sauce and hot sauce. Season with salt and pepper. Refrigerate until ready to use.
For the remoulade: Whisk together the mayonnaise, capers, cornichons, parsley and lemon zest and juice in a small mixing bowl. Season with salt and pepper. Refrigerate until ready to use.
For the salad: In a medium mixing bowl, add the onions and lime juice. Let stand for a few minutes. Add the lobster meat, avocados and cilantro. Mix together well and season with salt and pepper.
Divide the shredded romaine lettuce evenly into 4 martini glasses. Place the lobster avocado salad on top of the lettuce. Top with 1 tablespoon of cocktail sauce and remoulade sauce. Garnish with romaine hearts, lobster claws and lemon wedges.