Place the crème fraîche in a food processor with the anchovy fillets, Parmesan and lemon rind and juice. Blend to make a smooth dressing and season to taste with pepper.
Tear the lettuce into bite-sized pieces and place in a bowl with the avocado. Pour over the dressing, toss together and divide between 4 bowls.
Arrange the chicken on top and scatter with the croûtons. Season with pepper and sprinkle with a little Parmesan. Serve immediately.