1. Squeeze the juice from the lemon into a bowl of water. Working with 1 artichoke at a time, break off the stem and snap off the dark outer leaves. Using a serrated knife, cut off the remaining leaves at the top of the base. Using a small, sharp knife, trim the base. Using a spoon or a melon baller, scoop out the hairy chokes. Rub the artichoke bottom all over with the cut lemon and drop it in the water.
2. In a medium saucepan, combine the olive oil, wine, water and garlic and bring to a simmer. Add the artichoke bottoms and a large pinch of salt and simmer over moderately low heat until tender, about 12 minutes. Let the artichokes cool slightly in the cooking liquid, then add the 2 teaspoons of lemon juice and season with salt. Serve warm or at room temperature.
Make Ahead: The artichokes can be refrigerated overnight. Rewarm gently in the oil before serving.
Serve With: Toasted peasant bread.