Place each branzino on a cutting board. Cut off the top and side fins using scissors. Arrange 3 even piles of the lemon slices, 2 sprigs thyme and 2 sprigs rosemary in a cast-iron skillet large enough to hold all 3 fish (or use smaller cast-iron skillets large enough to hold one fish each). Lay a fish on top of each pile in a standing position so that the open cavity is resting on the lemons, and herbs. Set aside.
Combine the salt, egg whites and dried thyme in a large bowl to form a grainy paste. Press a 1/4-inch layer of the salt mixture onto each fish until they are completely encased.
Place the skillet or skillets in the oven and roast until an instant-read thermometer registers 135 degrees F when inserted into the thickest part of the fish, about 20 minutes. Let stand 10 minutes. Use a large spoon to break open the salt mixture—you will need to apply a little force—and peel the salt layer off.