Good information aand Ican verify the census records for 1790 and 1800 in South Carolina for Lee and Gershom. This Gershom is my ancestor. In the 1800 census other than Lee and Gershom you also have Lee Allen two brothers Isaac and Squire Allen. Not long after the 1800 census and probably by 1802 or at least by 1804 -1808 you will find all four Allens on the Tax list namely Lee, Isaac, Squire and their father Gershom in Warren County Kentucky by 1810 my Squire was in Randolph County Illinois in the part that became Johnson County later. Squire was in Arkansas before 1820.
I knew I couldn't find Lee in the 1830 census of Kentucky so this explains if he was in Indiana why Icouldn't find him.
I went and checked the Dixon Allen out that was in Hunt County Texas. This Dixon I believe is the same Dixon. Ancestry.com says he was 43 and born in South Carolina but I'm thinking it may be 48. It doesn't look like the rest of the 3's on that page but also it doesn't look like an 8 either. What is interesting is not necessarily his age but that he was born in South Carolina and in his household was probably a daughter Manervia L. age 13 born in Kentucky which puts her born in 1837. We know that Lee came from South Carolina and was there in 1800 and that he went to Kentucky and that he had a son Dixon and the Dixon in Hunt was born in South Carolina and Manervia that was in his household was born in Kentucky. He seems to be the same one. He could have very well left for Texas after 1845 and after the deposition was given.
I think this is the same Dixon What are your thoughts.