Person_id | employee_id | appointment_time
----------+-------------+-----------------
int       | int         | date

SELECT
  qLast.person_id,
  qLast.employee_id,
  qLast.LastDate,
  qPrevious.employee_id,
  qPrevious.PreviousDate
FROM
  (
    SELECT
      app.person_id,
      app.employee_id,
      Max(app.appointment_time) AS LastDate
    FROM
      app
    GROUP BY
      app.person_id,
      app.employee_id
    HAVING
      app.person_id <> 0
      AND app.employee_id = 235
  ) qLast
  LEFT JOIN (
    SELECT
      qSub.person_id,
      app.employee_id,
      qSub.MaxOfappointment_time AS PreviousDate
    FROM
      (
        SELECT
          app.person_id,
          Max(app.appointment_time) AS MaxOfappointment_time
        FROM
          app
        GROUP BY
          app.person_id,
          app.employee_id
        HAVING
          app.person_id <> 0
          AND app.employee_id <> 235
      ) qSub
      INNER JOIN app ON (
        qSub.MaxOfappointment_time = app.appointment_time
      )
      AND (qSub.person_id = app.person_id)
  ) qPrevious ON qLast.person_id = qPrevious.person_id;