Information from cousins on the web place my Eliza Jane as the daughter of Francis J, "Franklin" Hambrick (b abt. 1827 near Princeton, d. Bef. 1860 near Princeton). Eliza's mother was Frances M. Smithey (b. abt. 1828 and d. bef. 1860 near Princeton). Eliza and an only sibling, William Ross Cash Hambrick (b. 1845 Madison County, Alabama) are named in the will of Franklin's father, Greenberry Hambrick (b. 1790 in Burke County, NC and d. June 6, 1865 near Princeton). Eliza and William are orphans when the will was dated in 1860, therefore the dates of death for Franklin and Frances are established. Greenberry has a large marker in his family cemetery in Hambrick Sinks, a gulf in the mountains about halfway between New Market and Princeton. Franklin's mother was Elizabeth "Betsie" Damron(b. abt. 1791 in Jefferson, Tennessee and d. abt. 1871 in Jackson County, Alabama.
Greenberry Hambrick had a brother named Joseph V. Hambrick (b. Sept. 10, 1797 and d. Mar. 21, 1877 near New Market, Madison County, Alabama. Joseph had a large family by several wives. Joseph and many family members are buried in his family cemetery (Hambrick Cemetery) about 3 miles ESE of New Market, just south of Backbone Mountain.
Your Lee Calvin and Joseph Frank almost certainly descend from one of these 2 brothers. The parents of Joseph and Greenberry were Robert Hambric/Hamrick (1755 - 1824) and Hannah Hubbard (1765 - 1808).
There are many Hambrick researchers with better information than I and they are active on this forum. I'll bet if you post a new querry you will meet a few of them in a day or so. I will introduce you to some if you will contact me directly. I do not want to "air out" our e-addresses on the forum unprotected, but you can follow a link to get my e-address securely on this or other genealogy forums including Fitch, and Payne.
I will be glad to share what I have about Eliza Jane Hambrick and her descendants. I knew several of them.