In a medium bowl, whisk together the egg, mayonnaise, Dijon mustard, Worcestershire sauce, Old Bay, lemon juice, parsley, and optional hot sauce until smooth.
Add the crab meat, panko breadcrumbs, cracker crumbs, celery, and green onion.
Fold gently with a rubber spatula until just combined. Avoid overmixing so the crab meat stays in large pieces.
Form into 4 crab cakes about 1 inch thick. Press just firmly enough for them to hold together without compacting the crab.
Place the crab cakes on a parchment-lined tray and refrigerate uncovered for 30 minutes.
Heat oil in a cast iron or heavy nonstick skillet over medium heat until shimmering.
Carefully add the crab cakes and cook for 4–5 minutes per side until golden brown and heated through. Flip only once using a thin fish spatula.
Stir together all lemon dill sauce ingredients in a small bowl.
Butter the buns lightly and toast until golden brown.
Spread a thin layer of lemon dill sauce onto both sides of each bun.
Layer lettuce, tomato, crab cake, red onion, and pickle chips onto the buns.
Serve immediately while crispy and hot.