Put the potatoes in a large pan of cold water. Bring to the boil, then simmer for 12-15 minutes until tender. When there are 4 minutes of cooking time left, add the beans and petits pois. Drain, reserving 300ml of the cooking water. Cut the potatoes into smaller pieces.
Put the cherry tomatoes in a bowl with the parsley and the cooked potatoes, beans and peas. Season with freshly ground black pepper.
Meanwhile, heat the oil in a large frying pan and cook the chicken fillets and gem lettuce halves for 4-5 minutes on each side. Pour in the reserved veg cooking water along with the lemon juice and continue to cook, covered, for 4 minutes. Remove the chicken (make sure no pink colour remains) and lettuce from the pan, then stir in the mustard to thicken the sauce slightly.
Slice the chicken and serve with the braised lettuce and potato mixture, with a drizzle of mustard sauce over the top.