using www.google.com and "advanced search" , and "exact phrase" I typed in Landon C. Allen - several "hits" came up as follows:
Landon C. Allen b. 6 Jun 1819 in Nelson County, Va married Mary Ann Thacker b. @ 1828 Nelson County, VA.
father of L.C.Allen:
William Allen (1749-1838) married Dorothy Bailey ("Dolly") b. (@1786-after 1866)
married 17 Aug 1854 Putname Co, VA
this matches up with the LandIn (not Landon) C. Allen and wife Mary in the Tom, Benton, MO 1880 US Census. In that census LanIn C. Allen is shown as born 1819 VA and parents both born VA, which matches above information.
There is other information on www.google as above - but I did not pursue it.
The above information was shown as being from the 1850 Census in Kanawah Co, VA -
Hope this helps - but you may already have this information. I did not see information on the children of Landon C. Allen and wife Mary.