Season the monkfish with 1/2 teaspoon celery salt, 1/4 teaspoon kosher salt and a few grinds of pepper. Melt the butter in a large nonstick skillet over medium-high heat. Add the monkfish and cook until golden brown and cooked through, 4 to 6 minutes per side. Transfer the monkfish to a cutting board and cut into 1-inch pieces. Let cool.
Meanwhile, whisk the mayonnaise, the remaining 1 teaspoon celery salt, the lemon zest and juice, celery leaves and a few grinds of pepper in a medium bowl. Refrigerate until ready to serve.
Toast the rolls and line the insides with lettuce. Add the monkfish, chopped celery and chives to the bowl with the mayonnaise mixture; gently toss. Divide the monkfish salad among the rolls. Serve with pickles and the potato chips.
Most monkfish fillets are sold skinless with the membrane removed. If your fillets have a membrane, remove before seasoning.