Rinse the hens and pat completely dry, inside and out, with paper towels. Let stand at room temperature for 1 hour.
Preheat the oven to 200 degrees F. Place a large wire cake rack over a jelly roll pan or cookie sheet with sides. In a stockpot, melt shortening over high heat to a depth of 2 to 3 inches and heat it to 375 degrees F.
Carefully put 1 Cornish hen in the hot oil. Deep fry, turning occasionally, until golden brown, about 12 minutes. To check for doneness, using a wire mesh skimmer (slotted spoon is fine) and tongs, carefully remove the hen from the stockpot and insert instant-read thermometer in the thickest part of the thigh, not touching the bone - it should read 180 degrees F. Transfer to wire rack and keep warm in oven while frying the other hen. Let the second hen rest for 5 minutes after removing from oil.
Serve whole, or use a cleaver to split the hens lengthwise. Serve with the salt, pepper, and lemon wedges, letting each person season his or her hen to taste.
Don't fill your stockpot more than half full with shortening or oil, to allow for the inevitable boiling up when the hens are added. Also, be sure the hens are at room temperature so the fat temperature doesn't drop dramatically from the shock of an ice-cold bird.