Okay - still looking but just a hunch here, have the records for Preston Conn been checked for Lydia's birth around 1760-1771...reason I ask is it possible she is the daughter of Andrew Huntington; who's son (Lydia had a brother) Enoch who died 4 yrs of age:
http://search.ancestry.ca/iexec/?htx=View&r=5543&dbi...
named from his uncle and died in Preston for which she might have named her own son?
Far-fetched but just thinking outloud : )