Clean the zucchini, slice lengthways with a peeler and blanch in boiling salted water for about 1 minute. Drain the slices on a kitchen towel.
Cut the mushrooms into wafer-thin slices. Mix the lemon juice with water, olive oil, salt, pepper and sugar.
Arrange the zucchini and mushrooms on plates like scales and drizzle with the sauce. Use a peeler to slice the parmesan and pour over it. Garnish the carpaccio with a few basil leaves.