Clean, peel and coarsely grate the carrots and beetroot. Mix vinegar, lemon juice and mustard. Season with salt, pepper and sugar. Whip the oil into it. Wash the chives, dab dry and cut into small rolls, except for a few stalks for garnishing.
Add to the vinaigrette and mix. Mix the grated carrots and beetroot and the vinaigrette and leave to stand for a while. Wash and clean the lamb's lettuce and arrange on plates with the beetroot and carrot salad.
Serve garnished with remaining chives.