I think this answer is lost to time.
JohnP's answer sources from "The Fundamentals of Pa Kua Chang, Volume 1" by Park Bok Nam and Dan Miller. Park Bok Nam is Lu Shui Tian's successor, and Dan Miller was Park's student and also the editor of the Pa Kua Chang Journal (1990-1997). This book does not mention a 500 year old lineage source. It does say that Lu preferred the teaching of his first teacher.
Lu told Park that his first teacher, Li Ching-Wu taught a more complete martial arts system than his second teacher because it combined straight line Pa Kua methods with the circle walking forms and maneuvers.
According to Master Park's book, Lu Shui Tian (1894-1978) trained in bagua in his youth, and fled to Korea during the Second Sino-Japanese War (1937-1945), though even the year is unspecified. To find another primary source with more information, you probably need to find someone who trained with Lu Shui Tian in China before the war and also survived the war. They would probably be 100 years old by now.
Also according to Master Park's book: the stellae at Dong Hai Chuan's gravesite list the Korean branch of the lineage with Lu Shui Tian as the only member of its 5th generation.
No known bagua lineage predates Dong Hai Chuan (?-1882)
Park's lineage almost certainly does not trace back to a 500 year old source that is not Dong Hai Chuan. Park himself does not claim this, and the scholarship on this subject currently points to Dong Hai Chuan as the founder, even among bagua schools that claim other sources.
If you are really interested in the origins and lineage of baguazhang, I recommend starting from the Pa Kua Chang Journal (1990-1997). The publication contains interviews with masters and contributions from many of the major figures in bagua and xingyi of the time. The publication was quite dogged about pursuing everything about bagua; I would describe it as everything you never wanted to know about bagua.
Miller and one of his sources were both wildly enthusiastic about researching bagua's origins, as described in Volume 3, Number 1 Nov/Dec 1992:
The primary source of this information is taken from the work of Professor K'ang Ko-Wu of Beijing. While working on his master's degree in 1980-81, Professor K'ang wrote his thesis on the "Origins of Pa Kua Chang." ... Professor K'ang's research was extensive and involved close examination of over 650 documents from the Ch'ing Palace history books and over 230 papers written on martial arts. He also examined the situations of 413 teachers in 24 provinces and cities, personally investigating in 16 cities and counties and 9 provinces. K'ang interviewed over 256 people resulting in over 274 documents. Many of the people he interviewed were elderly boxers of the older generation who spoke openly about their martial art.
In Volume 3, Number 4 May/June 1993, they basically conclude that there is no solid evidence of a bagua source other than Dong Hai Chuan, though Miller leaves open the possibility. K'ang believes Dong Hai Chuan was the sole originator.