Prepare the artichoke stem: Pull any leaves off the stem, and use a vegetable peeler to peel off the stem's woody exterior. Use a sharp stainless steel knife to trim off the end of the stem and gently score the trimmed end with an "X" pattern. Rub the stem all over with the cut side of one of the lemon segments to prevent browning.
Prepare the artichoke bud: Cut off the top quarter off the artichoke, about 1/2-1 inch. Rub the cut leaves all over with the lemon. Use kitchen shears to snip off the pointy tips of the remaining leaves.
Steam the artichoke: Fill a large pot with 1 inch of water, and squeeze in any remaining lemon juice. Add the squeezed lemon segments to the pot. Place a steamer basket in the pot, add the artichoke, and bring to a boil. Cover and steam for 35-45 minutes, or until the artichoke stem is fork-tender and you can easily peel off the outer leaves.
Remove the choke: Allow the artichoke to cool slightly. Slice it in half lengthwise, and use a small spoon to scoop out the hairy choke.
Serve the artichoke halves with melted butter or another dipping sauce of your choice. To eat, dip the leaves into the sauce and use your teeth to scrape off the meat, discarding the tough, fibrous shell. You can eat the artichoke heart and stem in their entirety.