Noam Silberberg, a fifth cousin of Blossom, provides the following geneological information after locating her story online.
The head of the family was Eliahu Lerman (born around 1830) who was a well known rabbi in Pulawy and later in Wiskitki. According to the information I've collected, Eliahu was actually born "Eliahu Topel" and changed his name to avoid military service, probably in the 1850's. This is a little known fact and many sources claim his father was also a Lerman, which is not true.
Eliahu's father was Abram Jozepa Topel who was known as the Saraf of Konskowola. According to books written by Eliahu Lerman (and which are available online), Abram Jozepa was the son of Benjamin who came from Lithuania.
Eliahu had 4 sons that I know of: Abram Jozepa, Chaim, Nachum and Israel. All except for Nachum were rabbis in different Poland towns.
Israel was a rabbi in Kosow Lacki and the father of Blossom's grandfather Abraham Lehrman. I recently contacted a great grandson of Chaim Lerman (Blossom's 3rd cousin) in Massachusetts and he was able to fill many of the gaps on his branch.
I am a descendant of Eliahu's brother, Jakow Icek Topel, who was a rabbi in Solec nad Wisla. I found out about my connection to the Topel family only a few months ago thanks to a document I found on a trip to Poland.