Thank you Bill, for your interest and your post. I am thinking that some of the data that you listed may have come originally from me in that I was communicating with Wayne Julian in the Fall of 2001 and had given him the impression that Lydia Mariah Jacobs Frieze had possibly migrated to Missouri following her first husband's death in 1863. Therein lies the mystery as to which Lydia M. Frieze it was that married Thomas H.B. Julian. (I had given this information to Wayne Julian who I think may have transfered it to you, if I didn't actually do that myself as you and I communicated via email in Dec 2001).
Anyway, here is the mystery. There were two Lydia M. Friezes. Mine, who as you know was a Jacobs by birth and who was born in Abt. 1837 in Jefferson County, TN and who migrated with her father's family to Pope County, IL in about 1849. She would later marry Anderson C. Frieze, thus becoming Lydia Mariah Frieze.
Another Lydia M. Frieze, born Abt. 1847 to William Babb Frieze and his wife. William Babb Frieze was the brother to Anderson C. Frieze and that would make the second Lydia M. a neice of my Lydia Mariah (even though my Lydia was only Abt. 10 years old at the time). [Note: I would have said that the daughter of William Babb Frieze was a name sake of my Lydia but the two families would have had to have known each other in Tennessee as the migration to Illinois did not take place until the second Lydia was about 2 y/o. Since the Frieze families were from Greene County Tennessee and the Jacobs families were from Jefferson County, Tennessee (neighboring and connecting counties) this was not impossible but is not proven, thus merely speculation at this time.]
Neither Wayne Julian nor I know for sure which Lydia M. Frieze it was that married Thomas H.B. Julian. However, it was noted by Wayne Julian that the wife of Thomas H.B. is buried in Portales, New Mexico and it is her grave stone that gives a birth year of 1847. Thus, leading one to think that the wife of Thomas H.B. was the second Lydia M. rather than my own Lydia Mariah.
I have queried Tracye Brewer who is a Frieze researcher and whose direct ancestor was the brother of the second Lydia M. Frieze, but Tracye does not know anything more than we know about Lydia M. Frieze.
One of the factors that might tell the tale on this mystery is what might have happened to the three children of Lydia Mariah Jacobs Frieze who were the children of Anderson C. Frieze, b. (1834-1863). Those children were John W. Frieze b. Abt. 1855; Caleb A. Frieze, b. Abt. 1858; and Sarah E. Frieze, b. Abt. 1862. I know of these three from a census record listing them living with the their grandmother in about 1870 in Pope County, IL. If these children can be located in Texas or New Mexico (later on in chronology) then it would be logical that they too went West with their mother and her new husband, Thomas H.B. Julian. While this would be an indicator, we would be closer to the truth as to who exactly the wife of Thomas H.B. really was and what too happended to my Lydia Mariah Jacobs Frieze, as we do have proof that she did apply for a pension as the widow of Anderson C. Frieze and her application came from somewhere in Missouri.
Until such time as we can conclude with answers to these mysteries, I will hold in abeyance the notion that my Lydia Mariah Jacobs Frieze in due timing (1865) attached the Julian surname to her own. However, I am very grateful for your input.