Several researchers on Ancestry.com and elsewhere have tied together the Andrew Jackson Lawrnece, son of Thomas Lawrence in the 1850 Census in Tuscaloosa County, Alabama, with the Andrew Jackson Lawrence who died in Searcy County, Arkansas in 1923. However, other than some threadbare circumstantial evidence (1. He has the same name, and 2. He died in Arkansas), there is no solid evidence or proof that connect the two Andrew Jackson Lawrence's together as the son of Thomas Lawrence, while there is a wealth of evidence to the contrary.
1. First and foremost, Andrew is not listed in Thomas's probate records. The records, which I have a copy of, give a very extensive and complete list of all of Thomas's living children. The deceased children, Emeline and Mary, are not named in the records. As Andrew is not named either, it is safe to assume he likely had died before Thomas died in 1860. Now yes, it is POSSIBLE, that Andrew was a "Black Sheep" and written out of the will and exiled from the family, but there is nothing to substantiate this theory in the least. Andrew has not been located for the 1860 Census; in fact, neither of the Andrew's have been located for that census.
2. The 2 Andrew's appear to have a 5-year age difference, which is significant. Thomas's son Andrew in 1850 is 10 years old, so he was born circa 1840. The 5 confirmed Censuses of the other Andrew have him born in: 1846, 1844, 1845, 1847, and 1846 (from 1870 to 1920, respectively). Now clearly the Census records rarely give a precise age or year of birth, but to see the age difference being about 5 years apart very consistently points to it being unlikely that the 2 Andrew's are one in the same.
3. Those same 5 aforementioned Census records also say that the second Andrew was born in Georgia, while Thomas's son Andrew was born in Alabama, as were all of Thomas's children back to Elizabeth [Dollar]. Only Thomas's 3 oldest children were born in Georgia. The rest were very consistently born in Alabama.
4. The Lawrence clan appear to be a very tight-knit group they travel in clans, and settle the same general areas together. Out of all of Thomas's children, only Nancy [Burchfield] remained behind in Tuscaloosa County permanently when Thomas left for Arkansas; Matthew stayed for a while, but eventually moved to Arkansas as well. Bryant and Tabitha [Burnside] (and possibly Elizabeth; she has not been located in the 1850 Census)set off first for Arkanas before their father and siblings, but once his Thomas arrived in Independence County, Bryant moved there to be near his family; Frances Jane [Gilbert], Benjamin, Martha [Bragg], William, and Joseph also settled in Independence County. Tabitha remained in Union County, Arkansas, but was joined by her brothers James, George, and Thomas, and her sister Matilda [Howard]. Sarah Elizabeth [Sain] took her time getting to Arkansas, but eventually settled in Howard County, where she was joined by her brothers Thomas and Matthew. Some of the siblings moved around, but eventually settled somewhere around Independence County, in either adjacent counties or 2 counties away, fairly near their siblings (this exludes those who remained in Union County, but they remained together nonetheless). Benjamin and Joseph died in Lawrence County (adjacent to Independent), which is also the last place we find France Jane; Robert died in Cross County, also adjacent to Indepence County. William died in nearby Craighead, but was buried in Independence. Matthew is last found in Pike County, which is adjacent to Howard County where Sarah Elizabeth and Thomas died.
As you can see, this family tends to be fairly tight-knit. This Andrew Jackson Lawrence, however, never lives near Thomas Lawrence's children. In 1870, he is in Cocke County, Tennessee. In 1880, he is in Green County, Missouri. From 1900 to 1920, he is in Searcy County, Arkansas. In all of the research I have done on Thomas Lawrence's children, I have not found them settled in Searcy County or ANY of the counties adjacent to Searcy. It's within the realm of possibility that this could further the "Black Sheep" stipulation, but again, this does not seem very likely.
5. In 1907, Andrew Jackson Lawrence of Searcy County, AR applies for a Confederate pension based on his service in Company A of the 23rd Georgia Infantry. Company A of the 23rd Georgia were called the "Bartow Yankee Killers", as the men of the company were recruited from Bartow County, GA. In the 1860 Census, there is only one A.J., Andrew J., or Andrew Jackson Lawrence in the entire 1860 Census, and was living in Chattooga County, and was the son of Martin Lawrence. This cannot be the Andrew Jackson Lawrence of Searcy County, AR because the A.J. Lawrence of Chattooga County served in the 34th Georgia Infantry, as proven by his service records, and continued living with his parents in the 1870 Census, and lived nowhere else than Chattooga County and died there. So while he is not located in the 1860 Census at all, the Andrew Jackson Lawrence who died in Searcy County, AR clearly must have lived in or very near Bartow County (which was Cass County until 1861) at that time. Now if he was the son of Thomas Lawrence, why on earth would he move from Tuscaloosa County where almost his entire family were, to Bartow County, Georgia, to Tennessee, to Missouri, and then finally to a place in Arkansas that was nowhere near any of Thomas Lawrence's other children?
After looking at each of these 5 factors, I believe it's clear that Thomas Lawrence's son Andrew Jackson Lawrence, and the Andrew Jackson Lawrence who died in Searcy County in 1923 were two distinctly different people, and I do not believe their information should be merged as if they were the same person on this site or any others.