Wash and trim the hard ends of the leaves of the artichokes, and remove all bruised leaves. Cut the artichokes in half.
Drain the oysters and rinse them. Strain and save all the oyster water, and add enough plain water to make six cups in a saucepan. Add the artichokes, lemon, onion, thyme, bay leaves, salt, and pepper. Simmer for 40 minutes.
Remove artichokes from the liquid. When cool, remove leaves, separate hearts and bottoms, and dispose of the choke. In a food processor or blender, puree the soft meat from the leaves. Pull apart the hearts. Dice the bottoms finely.
Make a light roux from the butter and flour. Whisk this into the liquid and return to a boil. Add the pureed artichokes and boil for 10 minutes.
Chop the oysters coarsely, reserving a dozen the big, good-looking ones.
Strain soup through a fine sieve into a clean pot. Add the chopped oysters, the leaves from the hearts, the diced artichoke bottoms, salt and Tabasco to taste. Heat to a simmer, then add the whole oysters. Simmer two more minutes, then serve.