The existence of the 14th Baron Tennington, and his familial relationships, may be inferred from Philip José Farmer's Tarzan Alive.
"Bunny Tennington" (Rutherford), 15th Baron Tennington is Tarzan's first cousin on his mother's side. She is the daughter of Edward Rutherford, 13th Baron Tennington and his wife Marguerite Blakeney.
Therefore the 14th Baron is most likely to have been the son of the 13th Baron and father of the 15th.
Wold Newton scholar Mark Brown has identified a novelist by the name of Rutherford, who appears in the novel Lost Horizon by James Hilton, as the younger brother of the 15th Baron. We may therefore safely assume that he is also the son of the 14th Baron.