Fill a large bowl with water and squeeze the juice from 3 of the lemon halves into the water, (the lemon water will keep the trimmed artichokes from discoloring*).
Hold an artichoke with the stem end toward you and pull off the very small bottom leaves. Working your way around the artichoke, bend back the lower leaves until they snap and break, then pull them off. Continue removing the tough outer leaves until you reach the cone of yellow inner leaves. Repeat with the remaining artichokes.
Cut the stems flush with the artichoke bottoms. Rub a lemon half over the exposed surfaces as you work. Turn each artichoke on its side and cut off the top two-thirds of the artichoke leaves, from the tip down to the meaty heart. Discard the trimmings.
Hold an artichoke heart in your hand, stem end down. Using a sharp paring knife trim away the tough dark green exterior all around the heart. Turn the heart stem end up and trim the bottom of the heart at a 45-degree angle to remove the dark green exterior and expose the light green flesh; rub all the cut surfaces with lemon. With a melon baller or sharp spoon, scrape out the fuzzy choke and discard. Drop the heart into the water and repeat with the remaining artichokes.
Drain the artichoke hearts and dry on paper towels. Cut each artichoke heart into one-half inch wedges. Heat the oil in a 10-inch fry pan over low heat. Add the artichoke hearts and a squeeze of lemon juice, increase the heat to medium-high, and cook, tossing the hearts, until tender and browned around the edges. Toss with the parsley and season with salt and pepper to taste. Serve garnished with the olives.