Cut off about 1 inch off the top of the artichokes. Remove any small leaves and trim the leaf tips. Trim the stem to make the bottom flat. Rub all cut portions with a lemon half.
Place the artichokes in a large pot, and add enough water to cover about half of the artichokes. Cut the lemon halves in half again, and add to the pot. Cover and simmer until the center of the artichoke is tender, 45 to 60 minutes. (Add more water as needed to keep the water level.)
Remove the artichokes from the pot and drain upside down on paper towels. When cool, remove the center and scrape out the fuzzy chokes. Chill for at least 2 hours in the refrigerator.
Combine the celery, sour cream, mayonnaise, dill weed, and garlic. Stir to blend. Chill for 2 hours.
Combine the cubed shrimp in the dressing.
Fill the artichokes with the shrimp mixture and place on individual serving plates lined with red lettuce. Garnish with mandarin oranges, putting some oranges between the leaves of the artichokes.