Peel and thinly slice the salsify. Place it in a soup pot and cover with cold water. Squeeze the lemon and add the juice to the pot. Bring to a boil, reduce to a simmer, and cook for 10 minutes.
Remove from heat and allow to cool slightly. Purée the mixture in a blender or food processor. Transfer the purée to the soup pot and add the milk gradually, until the desired consistency is achieved. Bring almost to a boil, then stir in the salt and white pepper to taste. Reheat thoroughly, but gently. Chop the chives to use as a garnish for each individual serving.
The salsify root has a faint oyster taste and looks a bit like an elongated turnip.