For the tartar sauce: Mix together the mayonnaise, relish, capers, dill, lemon juice, salt, pepper, sugar and onion in a bowl and refrigerate.
For the fish: Sprinkle the lemon juice over the fish fillets. Combine the milk, eggs, salt and pepper in a shallow bowl. Put the flour on a large plate. Combine the panko and seafood seasoning on another.
Heat 2 inches oil to 350 degrees F in a large Dutch oven.
One at a time, dip the fish into the flour, then the egg and milk mixture, then the panko. Set on another plate or small baking sheet. Place the fish in the oil and fry, turning once, for 3 to 4 minutes total (if you are using the shallow-frying method, cook both sides until golden brown, 2 to 3 minutes). Transfer the fish with tongs to a plate lined with paper towels or a wire rack set in a baking sheet. (I like to hit my fish with a little salt and lemon juice while it's hot.)
Meanwhile, toast the buns, by melting the butter in a pan and cooking them in it or by buttering the buns and broiling them until slightly golden.
Top the bun bottoms with the cheese and the fish, then spread the bun tops with tartar sauce and top your sandwiches.