Using apeeler, peel the cardoons starting from the bottom of the stalk, removing the tufts and the hard external ribs. You should only be using the internal ribs, which need to be rinsed and patted dry. Remove the filaments, squeeze the lemon into a bowl of water and lay in the cardoons.Cut the cardoons into pieces as long as your thumb from the tip of the nail to your hand.
Bring 4 quarts water to rolling boil and add 2 tablespoons salt. Add the cardoons and boil until tender, about 35 minutes. Remove the cardoon pieces form the water and allow to air dry.
Meanwhile, Fill a deep pot no more than halfway with extra-virgin olive oil. Heat oil over medium-high heat until it reaches a temperature of 360 to 375 degrees F. The oil should remain at or around this temperature throughout the cooking process.
Once the cardoons are dry, dredge them in the flour, through the beaten egg, and, finally, through the bread crumbs. Working in batches, fry the cardoons in the oil until golden brown. Use a slotted spoon or spider to gently drop the cardoons into the oil, being careful not to splatter the hot oil. Using the same spoon or spider, remove the finished cardoons to a serving plate. Serve immediately.