Remove the tough outer leaves of the artichoke and carve away the rough outer skin around the base and stem of the vegetable with a paring knife. Halve them and remove the chokes. Slice the artichokes and rub each slice with lemon. Soak them in a bowl of water with freshly squeezed lemon juice to prevent browning. Heat up 3 inches of extra-virgin olive oil in a pot with high sides to 350 degrees F. Remove the artichokes from the water and shake and pat off as much water as possible before dredging each slice into the beaten egg, and then into the flour. Fry immediately in batches in the hot oil until golden brown. Remove the artichoke slices from the oil, and place them on paper towels to absorb the excess oil. Season with salt immediately. Serve.