Heat the oil in a large skillet over moderately high heat until hot but not smoking. While the oil heats, stir together the cheese, flour and pepper in a wide shallow bowl, then lightly beat the egg with water in another wide shallow bowl.
Dredge 1 calamari steak into the flour mixture, shaking off the excess, then dip in the egg mixture, letting the excess drip off, and transfer to a plate. Dredge another steak in flour and dip in egg in the same manner, then sauté the coated steaks over moderately high heat, turning over once, until golden, about 1½ minutes total. Transfer to a platter and keep warm, loosely covered. Dredge, dip and sauté the remaining 2 steaks in the same manner, transferring to a platter.
Pour off the fat from the skillet, then add butter, lemon juice (to taste), and capers to the skillet and cook over moderate heat just until the butter melts, about 45 seconds. Pour the lemon caper sauce over the calamari steaks and serve immediately.