1. Remove the stalk from the bottom of each artichoke, so the artichokes can sit securely in the pan and on the plate.
2. Gently pull the leaves of each artichoke apart, and push garlic slices between the leaves.
3. Sit each artichoke on a lemon slice, and tie the lemon to the artichoke with string, knotting the string at the top.
4. Place the artichokes in a single layer in a deep saucepan, lemon side down. Season well, and pour the olive over the artichokes. Add sufficient cold water to ¼ fill the saucepan. Cover the pan with a thick, or double layer of foil, crimping the edges firmly to achieve a tight seal.
5. Bring to the boil, then reduce the heat to low and simmer for an hour, or until the artichokes are tender (to test for this, tug one of the large outside leaves gently - it should come away easily).
6. Remove the artichokes from the pan with a perforated spoon, and remove and discard the string and lemon. Push the leaves apart once again, and pour the liquid in the pan over each artichoke. Serve hot, or at room temperature.