Pawel Sygowski and Andrzej Trzcinski from the University of Lublin wrote a very relevant article in Polish about the Jewish cemetery in Lubaczow . In particular they concentrated on the graves from before 1800, those graves that I in my own survey, usually had no ability to write more than "Old grave" and perhaps take a photo of the top of the gravestone that I could see. Their article was published in the Rocznik Lubaczowski Tom III in Lubaczow in 1998.
I will come back to this article, but for now I want to concentrate on three graves that Pawel Sygowski and Andrzej Trzcinski have listed. Perhaps descendants of this rabbinical family or others with knowledge about rabbis and religious leaders will be able to identify the family.
In the year 1797 Rabbi Noach Avraham died. He was buried in Lubaczow. This happened in the Hebrew month of Elul. His gravestone does not mention the name of his father.
In the year 1796 or 1797 Rebbetzin Devorah died. She was buried in Lubaczow. Her grave does not give the name of her father, but tells that she was the wife of the head of the rabbinical court in Lubaczow.
A few years before (1793?) their son Aharon Shmuel died on Adar 19th. On his gravestone it says that his father was Rabbi Noach Avraham, the head of the rabbinical court in Lubaczow and that Aharon Shmuel died "tender in years" רך בשנים.
We must assume that Rabbi Noach Avraham and Rebbetzin Devorah had other children and that there may be living descendants from this family.