1.. Place the artichoke in a lidded saucepan with enough water to cover it (usually about 2 quarts). Squeeze the juice from half of the lemon into the water; toss the squeezed lemon into the pot. Bring to a boil.
2. Lower the flame to a simmer, cover the pot, and cook until a fork comes easily out of the stem when poked, usually about 45 minutes. Drain.
3. Squeeze the remaining half of the lemon into the melted butter, and mix well with a fork or whisk. Peel off the outermost 6 or 7 leaves and discard them.
4. Dip remaining leaves in butter, eating edible parts, working your way in to the entirely edible heart.