In a shallow dish combine the flour, 2 tablespoons of the basil, and the lemon peel. Place eggs in another shallow dish. Dip chicken into flour mixture, then into the eggs, and then again into flour mixture to coat.
In a 12-inch heavy skillet heat cooking oil over medium-high heat. Add chicken breast strips to skillet. Cook, uncovered, for 6 to 8 minutes or until chicken is no longer pink, turning once. (If necessary, reduce heat to medium to prevent overbrowning and add more oil as needed during cooking.) Cool slightly.
Meanwhile, in a large bowl toss together the greens, radicchio, strawberries, and remaining 2 tablespoons basil. Drizzle vinaigrette over salad mixture; toss gently to coat. To serve, line individual bowls with lettuce leaves. Add salad mixture. Top with chicken and, if desired, basil leaves. Makes 6 main-dish servings.