Place the mayonnaise, sour cream, yogurt, cream cheese, scallions, dill, parsley, lemon zest, lemon juice, 2 teaspoons salt, and 1 teaspoon pepper in the bowl of a food processor fitted with the steel blade. Puree for a few seconds, until well mixed. Add the cucumber and puree for another few seconds, until combined. Pour into a container and refrigerate for a few hours to allow the flavors to develop.