Using a mandoline slicer or very sharp knife, slice the mushrooms as thinly as possible and arrange them in a single layer on a large serving platter. Scatter the arugula evenly over the top.
Just before serving, squeeze the juice of the lemon over the arugula and very lightly drizzle with some olive oil. Season with salt and pepper, to taste, and using a vegetable peeler, shave thin strips of Parmesan evenly over the top. Serve immediately.