To make pimento remoulade: In small bowl, mix mayonnaise, pimentos, mustard, pickles, pepperoncino, paprika, garlic powder, black pepper, lemon juice and hot sauce until well incorporated. Season with salt, to taste.
To make fried lobster tails: Preheat grill to 400 F and add oil to 10-inch cast-iron pan about 1/2-inch deep.
In medium bowl, whisk flour, 1/4 teaspoon salt, 1/4 teaspoon pepper, garlic powder and smoked paprika until well incorporated. Set aside.
In separate medium bowl, whisk egg, water and hot sauce. Set aside.
In third medium bowl, whisk potato chips, panko breadcrumbs and parsley until well incorporated. Set aside.
Cut lobster tails in half lengthwise, remove meat from shell and season with remaining kosher salt and black pepper.
Toss halved lobster tails in flour mixture first, egg mixture second then potato chip mixture third, coating thoroughly.
Fry lobster tails 3-4 minutes on each side until golden brown and cooked through. Close grill lid between flipping.
To make cheeseburgers: Preheat grill to 450 F using direct heat. Form ground beef into two 1/2 pound patties, each about 1/2-inch thick.
Using thumb, make dimple in center of each patty to help cook evenly.
Season both sides of burger with salt and pepper, to taste. Spread butter on each cut side of buns.
Grill burgers 4-5 minutes per side for medium doneness.
Add one slice cheddar cheese on each burger, close lid and grill about 30 seconds to melt cheese. Remove patties from grill to clean plate. Place buns cut sides down on grill grates and toast 20-30 seconds, or until well toasted, being careful to avoid burning.
To assemble: Place desired remoulade on buns. Place cheeseburgers on bottom buns. Top each with two fried lobster tail halves. Place handful shredded lettuce on lobster tails. Top with buns.