Pour 2 tablespoons of the lemon juice into a large bowl. Trim off and discard cores and any discolored leaves from endive heads. Cut each head in half lengthwise, then cut halves lengthwise into 1/4-inch-wide strips. As you cut the endive, drop the strips into bowl and mix with lemon juice to prevent them from discoloring.
Peel and core apples; cut into 2- to 3-inch-long, 1/4-inch-thick matchsticks, dropping into bowl and mixing with lemon juice and endive. Stir in parsley.
In a small bowl, mix the remaining 2 tablespoons lemon juice with the oil; add salt and pepper to taste. Pour over endive mixture and mix to coat.
Mound salad equally on plates. Pull any skin off smoked trout and discard; break trout into large flakes. Top salads equally with trout.