Welcome to G2G forum, Michael.
There is no doubt that the 1850 Census taker wrote a "T" as the initial of the middle name. Just compare it with the "T" in the name "Tennessee" in line 22 in the same Census sheet, or compare it with the "T" in "Texas" in any other line.
https://www.familysearch.org/ark:/61903/3:1:S3HT-XCC3-QN2
The listing made by the 1850 Census taker was not very accurate.
In line 31 there is a child named David J, 1 y/o, born in Texas.
This child is listed Daniel J, 11 y/o, born in Texas in the 1860 Census. See line 35 in the image below (Danl J).
https://www.familysearch.org/ark:/61903/3:1:33S7-9YB2-9FV3
Lewis J Hogue is listed in line 34 of the 1880 Census sheet below.
https://www.familysearch.org/ark:/61903/3:1:33S7-9YYY-932D
His son Daniel J (married at that time) is listed in line 25 in the same sheet.
I also found a death cert. of a Mrs. L M Hogue whose father's name is Lewis J Hogue.
https://www.familysearch.org/ark:/61903/3:1:33SQ-GY14-DV9B
Based on all of the above said, IMO the "T" in the 1850 Census is in error.