I have Littleton in my tree. I too believe that Littleton and Joseph were brothers. This is what I have on them.
Littleton West b. 26 Nov 1755 in Sussex Co. Del. Joseph West b. Joseph West b. 1 Dec 1762 Sussex Co. Del. By 1763 family was in Rockingham Co. VA. For about 12 years, then to Montgomery Co. VA in which that part became Greenbriar Co. VA (now WV).
Littleton had 400 acres on the head of Second Creek in Greenbrier Co. in 1780 by reason of settlement before 1778 on land adjoining Moses Turpin.
I find Littleton in Greenbrier Co. (W)VA on the tax lists for 1782-1786.
These are the marriages in Greenbrier by Rev. John Alderson. I think that these could all be siblings, but I don't have proof. This shows a connection between the West family and Turpins, who either lived close to each other in Greenbrier, or were "assignee of" each other in land transactons. Littleton West m. Elinor Gallaway, Feb. 6, 1781. Joseph West m. Agnes Carpenter, Feb. 17, 1781. Luke West m. Rosa Acers, Nov. 9, 1784. Penelope West m. Mitchell Porter, Jan. 25, 1788. Mary West m. Solomon Turpin, Mar. 18, 1788. Tabitha West m. William Kindir, Oct. 24, 1791.
Joseph is on the Mercer Co. KY tax roll for 1789 and Madison County KY 1792 Tax Roll. He moved to Wayne Co KY, but for some reason is not found on the tax rolls there, but rather on Garrard Co KY rolls for 1800 and 1810. In 1820 the numbers are listed as 3321-10010-00.
Littleton is found in Wayne Co KY in 1810 with the following numbers for his family 21001-11111-01. He must have moved to Madison Co. shortly thereafter as his daughter, Jane West, married John Turner in June 1814. Littleton gave his permission.
I have Littleton moving to Ray Co. MO with his daughter and son-in-law John Turner. I find him on an 1821 Tax Assessor's list, in 1829 he's credited for poll taxes improperly assessed on him, in 1831 he's listed in a poll in Fishing River Township voting for judges and a constable, and in 1833 he applies thru the Ray Co. Court for a Rev. War pension. I find nothing further on him. I don't know where he is buried, but his daughter and son-in-law are buried on land their family set aside and called "Siegel Cemetery", after their son, Thomas Turner's in-laws.
Droop me a line if you have any further information or questions. I might be able to dig up more info. Denice