Slice the fennel with a sharp knife or mandoline into paper-thin slices and the apple into thin strips. Mix them immediately with a little lemon juice so the apple doesn't brown.
Distribute the arugula over a plate and toss the fennel and apple through it. Scatter the smoked chicken strips on top so they're nicely distributed.
Whisk the olive oil with the mustard, the remaining lemon juice, salt and pepper into a smooth dressing and drizzle it over the salad. Coarsely chop the walnuts and scatter them on top last for a crispy bite and a light bitterness that goes well with the sweet apple.