Snap off and discard tough ends of asparagus; rinse spears. Pour water to a depth of 1 inch into a wide frying pan and bring to a boil over high heat. Add asparagus and cook, uncovered, until barely tender when pierced (3 to 5 minutes); drain. Immerse in ice water. When cool, drain again; arrange on a platter or on 4 salad plates.
Mix oil, tomatillos, and tomato; spoon over asparagus. Sprinkle with cheese and garnish with lemon wedges. If desired, season to taste with salt and pepper. Makes 4 servings.