Insert lemon and lemon thyme into the cavity of the fish.
Mix salt and egg whites together in a large bowl.
Spread 1/2 the salt mixture on a large baking sheet. Lay fish on top. Pour remaining salt mixture on top. Pack down tightly so fish is sealed in salt.
Reduce oven temperature to 400 degrees F (200 degrees C). Bake fish in the preheated oven until an instant-read thermometer inserted through the salt and into the fish reads 120 degrees F (49 degrees C), 15 to 20 minutes.
Cool fish for 2 minutes. Crack the salt coffin with a wooden spoon. Peel away the salt and discard. Transfer fish to a serving dish using 2 spatulas.