The David Abernathy to whom you are referring was b. 29 May 1726 in (then) Prince George County VA and baptized 6 Jun 1726. His will (dated 24 Aug 1808 in Lincoln County NC and apparently probated after his death in 1814) lists the children you cited, names his wife as Ann, but there is no Lucy listed.
I have never seen any contemporary documentation from his lifetime that proves a given name of Martha for his wife. I believe this may be an error from a mistaken cross-linking of some previous researcher's work, who apparently confused two or more different Davids, which, with these Abernathys, is all too easy to do.
Lucy was born Feb 14 1740, to a David & Ann Abernathy, but it has been determined that Lucy's father is the David Abernathy who, in 1727, purchased property in (then) Prince George County and in 1761 acquired property in (then) Dinwiddie County, married Ann Liles probably shortly after that first purchase of land, and died in Dinwiddie County VA in 1784. Dinwiddie Tax Records confirm a death year of 1783/4 since his estate began appearing in tax year 1784, and have also been of assistance in identifying her siblings (Clarissa or Clara who married Reese Rawlings, Ann whose son Baxter Mosley was given power of attorney to claim his mother's share of her father's estate, Signal whose 2nd wife was Martha Holmes, Aramanus who apparently never married and died young, David whose will is dated 1814 in Lunenburg County VA and possibly the William who is found in Mecklenburg County VA Tax lists from 1795 to 1804). We do not have a will for David Abernathy of Dinwiddie County, only indications of estate settlements.
Lucy was not a daughter of the David Abernathy who was only 14 yrs old on the date of her birth, but was the daughter of the David whose actual birthdate is unknown but has been estimated as no later than 1705/6 because he is assumed to have been at least 21 when he first purchased land in Prince George (later Dinwiddie) County, VA. He apparently resided in Bristol Parish area his entire life, but Lucy is the only one of his children whose birth was cited in the much abbreviated Bristol Parish Register.
Knowledge of the elder David's father's precise link to the Robert Branch to which the younger David belongs has been lost or destroyed, but DNA indicates he was very, very closely related, indeed! It has been speculated that the elder David was an Uncle of the younger one, but no evidence has survived to prove this, so it remains mere speculation.