In medium saucepan, bring 1 3/4 cups water to boil. Add rice; return to boil. Reduce heat to low, cover and cook until water is absorbed and rice is tender, about 20 minutes. Fluff with fork; transfer to bowl. Cool to room temperature. Cook asparagus in a large saucepan of boiling salted water until tender, about 1 minute. Drain and rinse with cold water to cool. Cut the asparagus into 1-inch pieces. Add asparagus, cucumber and green onions to rice. Whisk together mustard, sugar, vinegar, dry mustard, oil and chopped dill. Cover salad and dressing separately. Refrigerate until chilled. Pour dressing into salad and season with salt and pepper. Line large bowl with lettuce and mound salad in bowl. Garnish with dill sprigs.