Peel and julienne the celery root; steam about 4 minutes, or until crisp-tender. Plunge celery root into bowl of iced water to stop cooking and preserve crispness. Once cooled, drain well in colander and then on paper towels.
Meanwhile, julienne the green beans (or asparagus). Steam for about 3 minutes and then plunge green beans (or asparagus) into bowl of iced water to stop cooking and preserve crispness. Once cooled, drain well in colander and then on paper towels. *
Combine celery root, green beans, sweet peppers, onion, and chicken in large bowl. Stir well to combine.
Mix together lemon juice, mayonnaise, and yogurt until well blended. Stir into chicken mixture, coating well. Sprinkle minced parsley and basil over mixture; stir well again. Season to taste with salt and pepper.
Serve on lettuce or spinach leaves, if desired.