Preheat the oven to 350 degrees. Place salt in a baking dish and heat in the oven or 15 minutes.
Remove salt from oven, and increase temperature to 450 degrees. In the bottom of a roasting pan large enough for the fish, spoon about a third of the warm salt in the approximate shape and size of the fish. Lay 2 slices of lemon and three sprigs of tarragon on the salt. Lay the fish on top. Place the remaining lemon slices and tarragon on top of the fish. Spoon the remaining salt on top of the fish, patting it on the sides and making sure to cover it completely.
Bake the fish 10 to 12 minutes, or 8 minutes for each inch of thickness. Check for doneness by inserting the tip of a knife through the salt crust into the thickest part of the fish and wedging it slightly to see if the flesh is cooked.
At the table, remove the skin and fillet the fish. Pass the olive oil for sprinkling over the fillets.