I haven't found an index by name but there is one according to publishing date. The Farmer, I believed, was published on Fridays; so if you know the death date, you can browse the obituaries (they are in pdf format and the list contains only those issues which were available in their archives) of the Farmer shortly after the date of death. That link is:
http://www.sttammany.lib.la.us/cfdb/obits/Images/