Squeeze the lemon juice into a medium bowl of water. Working with 1 artichoke at a time, snap off the outer leaves and trim off all but 1/2 inch of the stem. Using a sharp knife, cut off the top two-thirds of the artichoke leaves. Peel the base and the stem. Using a spoon or a melon baller, scoop out the furry choke. Rub the artichoke heart with a lemon half and add it to the bowl of acidulated water. Repeat with the remaining artichokes and drop the lemon halves in the water.
Heat the olive oil in a medium saucepan. Add the onion and cook over moderate heat until softened, about 4 minutes. Drain and quarter the artichokes; add them to the pan. Season with salt and cook, stirring, for 2 minutes. Stir in 1 tablespoon of the parsley, add the water and bring to a boil. Reduce the heat to moderately low and simmer until the artichokes are tender and most of the water has evaporated, 25 minutes. Transfer the artichokes and their cooking liquid to a bowl; season with salt. Sprinkle with the remaining tablespoon of parsley and serve.
The artichokes can be refrigerated in their cooking liquid for up to 2 days. Reheat gently.