Into a small bowl, squeeze lemons, and set juice aside; discard lemon halves. Pull off tough outer leaves of artichokes, and discard. Trim tops and bottoms of artichokes, and discard. Slice in half lengthwise, and remove any fuzzy choke from heart of artichokes. Slice as thinly as possible, and toss immediately in lemon juice to prevent discoloration.
Brush any dirt off mushrooms. Trim base of stems. Thinly slice lengthwise, and place in a medium bowl. Remove artichokes from lemon juice with a slotted spoon and combine with mushrooms. Toss with olive oil, salt, pepper, and half the cheese. Divide among four salad plates, and top with remaining cheese.