In medium bowl, combine lemon juice, brown sugar, salt, pepper, and parsley. Slowly whisk in olive oil. Cut apple in half, core and cut into julienne slices. Add to dressing, stirring to coat.
Trim stem from the fennel bulb and set aside a few leaves for garnish. Cut fennel in half lengthwise and cut into very thin slices. Place fennel and radicchio in large bowl. Add apple mixture and half of the walnuts. Toss to combine.
Serve on a bed of Boston lettuce leaves; sprinkle with remaining walnuts. Garnish with the reserved fennel leaves.