Preheat the oven to 450.
Add the egg whites to the bowl of a stand mixer fitted with the whip attachment and mix on medium-high speed until soft peaks form, about 2 minutes. Reduce speed to low and fold in the salts until thoroughly combined.
Spread a thin layer of the salt and egg mixture on a large baking pan, about ½ cup. Place the fish on the pan and cover completely with the remaining egg and salt mixture. Using your hands, make sure the fish is completely covered and packed tightly, as if you were making a sand castle.
Bake for 25-30 minutes, remove from the oven and let rest for 10-15 minutes.
Using a wooden spoon or the handle of a chef knife, strike the crust to crack it. At this point you should be able to remove the salt crust in large pieces from the top of the fish. Carefully, fold the top half of the fish towards the spine and place on a serving platter. Divide the meat among 6-8 plates and finish with a drizzle of extra virgin olive oil and a squeeze of lemon.