Open trout, skin sides down, on a foil-lined baking sheet coated with cooking spray. Sprinkle salt and pepper evenly over fish. Arrange 2 tarragon sprigs and 3 lemon slices on 1 side of each fish. Fold fish over tarragon and lemon. Broil 6 minutes per side or until fish flakes easily when tested with a fork.
While fish cooks, chop remaining tarragon sprigs to equal 1 teaspoon. Combine 1 teaspoon chopped tarragon, mayonnaise, mustard, and garlic, stirring with a whisk. Serve fish with aioli. Garnish with tarragon sprigs, if desired.