Squeeze lemons into a small bowl. Set aside. Pull off tough outer leaves from artichokes and discard. Trim bottoms and tops of artichokes. Slice lengthwise and pull out the fuzzy choke, if any. Slice artichokes crosswise as thinly as possible and immediately place in lemon juice to prevent browning.
Slice mushrooms. Remove artichokes from lemon juice with a slotted spoon. Combine with mushrooms and dress with olive oil, salt, and pepper. Toss with half of the Parmesan and arrange on 4 salad plates. Garnish with remaining cheese, and serve.