James and Lydia had a daughter named Elizabeth. I'm not sure that there is a connection between this Hood family and the Elizabeth that married Joseph McGinty.
Proof that James married Lydia is shown below:
James McGinty is listed in the 1816 tax roll for Clairborne Co., MS, but is then missing from a later 1816 federal census where his wife, Lydia is shown as the head of the household. This census shows Lydia with one male over twenty-one, two males under twenty-one, two females over twenty-one and one female under twenty-one. Based on this, James could have died in 1816. Lydia is not found in the 1820 census, so she could have died before then. A member of the Tunis Hood family, Dellmann Hood, wrote a book titled The Tunis Hood Family: It's Lineage and Traditions. It mistakenly shows that Lydia Hood married Alexander McGinty, Jr., when in fact, she married James McGinty.