Preheat grill to high. Fill large bowl with water and add juice of one lemon. Cut the top 1/3 off of the artichoke. With scissors, trim the top portions of the remaining leaves to remove thorns. Cut stem leaving about 2" attached to artichoke. Turn the artichoke top-side down and cut through the stem to halve the artichoke. Cut again to quarter and remove fuzzy part of heart and center leaves with thorns [not much.] Immediately place in bowl of lemon water. Continue with balance of artichokes. Tear off a sheet of aluminum foil. Line up artichokes on foil, drizzle with oil, season with salt, and place lemon slices over. Tear off a second sheet of foil and place on top of artichokes. Crimp edges to seal and create a large pocket. Place on hot grill for 15 minutes. Tests doneness by inserting knife into thick portion of artichoke heart. You should feel a bit of resistance. Arrange on platter. Garnish with parsley. Can be served hot or at room temperature. NOTE: You can get similar results using your oven. Preheat oven to 400 degrees F and follow directions.