1. Combine lemon, next 3 ingredients, and 2 1/2 cups water in large Dutch oven. Place a steamer basket in Dutch oven.
2. Wash artichokes by plunging up and down in cold water. Cut off stem ends, and trim about 1 inch from top of each artichoke, using a serrated knife. Remove any loose bottom leaves. Trim one-fourth off top from each outer leaf, using kitchen shears.
3. Arrange artichokes in steamer basket. Bring to a boil; cover, reduce heat, and simmer 35 to 40 minutes or until stem end is easily pierced with a long wooden pick. Remove artichokes from Dutch oven. Let cool 15 minutes.
4. Preheat grill to 350° to 400° (medium-high). Carefully cut artichokes in half lengthwise; remove and discard choke. Liberally brush cut sides of artichokes with olive oil, and sprinkle with desired amount of salt and pepper.
5. Grill artichokes, covered with grill lid, over 350° to 400° (medium-high) heat 5 minutes on each side. Serve with Buttery Dipping Sauces or Mayo Mixtures. Garnish, if desired.