You probably have to create a keyword with an algorithm like:
(using DateTime Library)
My_serial_dates_list= List()
FOR i IN @{My_existing_list}
Add to List ${My_serial_dates_list} Convert Date to Serial ${i}
END
My_sorted_serial_dates_list= Sort Copy of ${My_serial_dates_list}
Should be Equal ${My_serial_dates_list} ${My_sorted_serial_dates_list}