Mix chicken, onions and walnuts in food processor bowl. Cover and process by using quick on-and-off motions until finely chopped. Add 1/3 cup of the poppy seed dressing; process only until mixed. Mix remaining dressing and the cream cheese spread in small bowl with spoon until smooth.
Spread cream cheese mixture evenly over entire surface of tortillas. Remove white rib from lettuce leaves. Press lettuce into cream cheese, tearing to fit and leaving top 2 inches of tortillas uncovered. Spread chicken mixture over lettuce. Sprinkle strawberries over chicken.
Firmly roll up tortillas, beginning at bottom. Wrap each roll in plastic wrap. Refrigerate at least 1 hour. Trim ends of each roll. Cut rolls into 1/2- to 3/4-inch slices.