In a medium or large bowl, whisk together the olive oil, lemon juice, and salt and pepper to taste. Taste for balance and adjust with olive oil or lemon as necessary. Using a mandoline or sharp chef's knife, slice the tomatoes as thinly as possible and arrange on a large platter. Season with salt and pepper and spoon a little of the vinaigrette over the tomatoes. Toss the lettuce with a little more of the dressing and arrange on top of the tomatoes.

Bring a large pot of water to a boil and add salt. Add the gnocchi and cook for about 90 seconds from the time they rise to the surface. Remove with a skimmer, drain well, and place in the bowl with the remaining vinaigrette. Toss gently, then scatter the gnocchi on the salad. Using a vegetable peeler, shave the cheese over the salad and serve immediately.