Fill a large bowl with water and squeeze the lemon halves into it; add the lemon to the bowl. Cut off all but 1 1/2 inches from the artichoke stems. Working with 1 artichoke at a time, pull off all the green outer leaves, leaving a cone of pale yellow leaves. With a sharp knife, cut off all but 1 1/2 inches of the leaves. Peel the stem and trim any tough green skin from the artichoke bottom with a sturdy vegetable peeler. Using a melon baller or small spoon, scoop out the hairy choke. Drop the trimmed artichoke heart into the bowl of water. Repeat with the remaining artichokes.