Implemented missing getTimeBefore(); Method by default return null. The key issue was in getting the previous run time when quartz-task hasn't yet been executed.

CustomCronExpression

public class CustomCronExpression extends CronExpression {
    private static final String DELIMITER = " ";
 /**
  * Constructs a new <CODE>CronExpression</CODE> based on the specified
  * parameter.
  *
  * @param cronExpression String representation of the cron expression the
  *       new object should represent
  * @throws java.text.ParseException if the string expression cannot be parsed into a valid
  *         <CODE>CronExpression</CODE>
  */

  public CustomCronExpression(String cronExpression) throws ParseException {
   super(cronExpression);
  }

  // here we can override this method and call it in future for the first-time 
  // lauch to get previous time
    @Override
    public Date getTimeBefore(Date targetDate) {
        Date nextFireTime = getTimeAfter(targetDate);

    Calendar calendar = Calendar.getInstance(getTimeZone());
    calendar.setTime(nextFireTime);
    calendar.add(Calendar.SECOND, -1);

    int dateUnit = getDateUnitCronExpression();

  switch (dateUnit) {
      case -1:
          break;
      case MINUTE:
          calendar.add(Calendar.MINUTE, -1);
          break;
      case HOUR:
       calendar.add(Calendar.HOUR_OF_DAY, -1);
       break;
      case DAY_OF_MONTH:
      case DAY_OF_WEEK:
       calendar.add(Calendar.DAY_OF_YEAR, -1);
       break;
      case MONTH:
       calendar.add(Calendar.MONTH, -1);
       break;
      default:
       calendar.add(Calendar.YEAR, -1);
       break;
    }

    Date previousDate = getTimeAfter(calendar.getTime());
    Date afterPreviousDate = getTimeAfter(previousDate);
    return findPreviousJobFireDate(afterPreviousDate, targetDate);
  }

  private int getDateUnitCronExpression() {
    String cronExpression = getCronExpression();
    if (StringUtils.isEmpty(cronExpression)) {
      return -1;
    }

    String[] expression = cronExpression.split(DELIMITER);
    return findDateUnitToWorkWith(expression);
  }

  private Date findPreviousJobFireDate(Date afterFuturePreviousDate, Date targetDate) {
    Date futureDate = afterFuturePreviousDate;
    Date resultDate = targetDate;

    while (true) {
      if (futureDate.equals(targetDate)) {
       return resultDate;
      } else {
       resultDate = futureDate;
       futureDate = getTimeAfter(resultDate);
       // prevent NPE and return current job time
       if(futureDate == null) {
         return resultDate;
       }
      }
    }
  }

  private int findDateUnitToWorkWith(String[] expression) {
   // * - represent the unit of date in cron expression
    // [0]Sec [1]Min [2]Hour [3]DayOfMonth [4]Month [5]DayOfWeek [6]Year
    for (int i = 0, n = expression.length; i < n; i++) {
      if (expression[i].equals("*")) {
       return i;
      }
    }
    return YEAR;
  }

}