Preheat grill to medium.
Measure a piece of foil large enough to hold the fish and coat it with cooking spray. Place a layer of lemon slices on the foil and lay fish on the lemon slices. Sprinkle with 1/4 teaspoon salt and top with tarragon sprigs.
Grill the fish on the foil (without turning) until it flakes easily, 12 to 20 minutes, depending on the thickness.
Meanwhile, whisk oil, lemon juice, chopped tarragon, mustard, pepper and the remaining 1/2 teaspoon salt in a bowl.
Toss lettuce with about 1/4 cup of the dressing in a large bowl; divide among 4 plates. Add beet and carrot to the bowl; toss with 2 tablespoons of the dressing. Divide the fish and slaw among the plates (discard the tarragon sprigs and lemon slices). Drizzle with the remaining dressing.
2 vegetable, 3 1/2 lean meat, 3 fat