Italian state civil records do not give cemetery information. If your ancestors are from a small town, there is probably only one cemetery in the town and the caretaker may be in the town's municipal bldg, or town hall. So best to contact the town hall in your ancestral town for specific info. Also, as in the above post, burials in Italy are not like those in the U.S. After so many years, the bones of the deceased are removed to make room for the newly deceased. These may be wrapped and buried in the same niche as the newly deceased, on top of its coffin, or placed in a communal grave in the cemetery, if there is no room.
So they may no longer be there at all. That's very sad. Hopefully, they were wealthy enough to be able to continue renting the plots. Being that they were all from Laurenzana, I should contact the town hall directly???
If your Italian town has microfilmed state civil death records for the ancestor(s) to which you are referring, there usually is an address for the house in which the person died, which may or may not be the house in which that person lived. Often the record will state that the death took place in the person's own habitation. However, for some of these houses, there is only a street name given and not a specific house number.