Slice the upper 2/3 of the leaves off the artichokes, then break off the remaining leaves, snapping them off at the base. Trim off the dark green stubs, going around the artichoke with a paring knife. Cut them in quarters, remove the fuzzy choke and slice each quarter into pieces 1/4-to-1/2-inch thick. As you work, rub the cut surfaces with lemon and put them in a bowl with the lemon juice and water to cover.