If you are suggesting Lydia is the child of Furman Applegate m. Sarah Ann Covenhoven/Conover, I think there is a bad age probem.They were married on 13 Sep 1840.Unless we have some pre-marital hanky-panky, Lydia would not have been born until May of 1841.That could just barely squeak in before the birth of the first child of theirs I know of--Nancy E Applegate b. 12 Jun 1842.
BUT, if Lydia died 30 June 1854, then she was she was just 13 years old.It is barely possible that she could have given birth at age 13, but just barely.
That's a pair of "barelys" right there.
The first name Furman isn't _that_ unusual in that time period.Without looking too hard, I see a Furman Updike, a Furman Thorn, and a Furman Clayton.And that doesn't count the men with Furman as a middle name.