In the meantime, trim the artichokes. Using a serrated knife, cut off the top third of the artichoke. Trim ¼ inch off of the stem. Use your hands to peel off the rough outer leaves on the lower section of the artichoke, to expose the tender and lighter leaves. Use a peeler to peel the artichoke stem. Use a spoon or a melon baller to scoop out the spiky “choke” in the center of the artichoke heart. Place the trimmed artichoke into the lemon water. Repeat trimming the remaining artichoke. Cut each trimmed artichoke into 8 pieces lengthwise.