I still don't understand how Johnson only got 13% in Mississippi. Any Democrat is guaranteed a floor of around 42% without winning more than 10% of whites.
Blacks were essentially disenfranchised in MS (and for the most part in AL) until the Voting Rights Act of 1965 (and even then it wasn't until the late 1970s that Blacks voted at near normal rates). Johnson probably won around 10% of the White vote, ranging from the 34.5% he won in Itawamba County (which was just 6.8% Black) to < 5% in many Black belt counties were Blacks were disenfranchised. In Jefferson County for example Johnson won 5% and 4 years later, Humphrey won 63%.
The Charts from "The Emerging Republican Majority":
Mississippi % of Pop 1960 % of Reg Voters 1964
Jefferson Country 68% 0%
Clairborne 70% 1%
Holmes 65% 0%
By State (1964)
Alabama 23%
Arkansas 49.3%
Florida 63.7%
Georgia 44%
Louisiana 32%
Mississippi 7%
NC 46.8%
SC 38.8%
TN 69.4%
TX 57.7%
VA 45.7%
I would say African-Americans were critical to LBJ in every state he won save for states were the population was too small to account for the margin of victory.
The best way to think about the black belt counties is that of a wealthy white elite dominating counties. You have counties with maybe 50,000 blacks of voting age, 30,000 whites of voting age casting only 5,000 white votes. Levels of disenfranchisement that reached 80% to 90% of all voters.
That is how Republicans could win the PV during the Solid South era. SC would go 90% Dem, but cast very few votes relative to its population, so it could be countered by a few extra percent in PA, NY and ILL.
Are these numbers the percentages of the white vote Johnson received in those states?
Based on these figures it seems certain that Johnson won the white vote in TX and AR and almost certainly in NC, while he lost it in VA and FL. TN may have gone either way.