Whisk mayonnaise, capers, parsley, juice, mustard, tarragon, 1/4 teaspoon salt, cayenne in bowl.
Sprinkle fish with remaining salt. Measure crumbs onto waxed paper. Whisk together egg and milk in bowl. Dip fish into egg mixture, then into crumbs, pressing crumbs onto fish to coat.
Heat oil in nonstick skillet. Add fish; cook, turning once, until golden brown and fish just begins to flake easily when pierced with fork, 6 minutes. Drain on paper toweling.
Layer bun bottoms with lettuce, fish, sauce and chips. Add bun tops.