Slice the fennel paper-thin, preferably using a mandoline or sharp knife. Slice the apple into thin strips and toss immediately with a splash of lemon juice to prevent browning.
Arrange the arugula on a plate and toss the fennel and apple through it. Slice the smoked chicken into strips and scatter over the salad.
Roughly chop the walnuts and sprinkle them over. Whisk the olive oil with the remaining lemon juice, mustard, salt and pepper to make a dressing and drizzle it over the salad just before serving.