I have reasons to suspect that the William King & Lidda Edwards who married in 1803 were not the parents of Moses & Nancy King. First, William & Lidda did not marry until 1803, so Lidda most likely would not have been the mother of children born 10-20 years before then. Isham Edwards is my ancestor and he was b. ca. 1755, so his daughter, Lidda would have been about the same age as Moses & Nancy, which would have made her much too young to have been their mother.
The Lightly King listed in the 1810 Franklin County, VA Census was not male, but female, age 45+, so she most likely was Lidda/Lydia, mother of Moses & Nancy, and probably a widow, and that is why her children were bound out in 1798. Only one King was listed in the 1788 Franklin Co VA Tax list - William King. In 1799, three Kings were listed: Matthew, Samuel & William. A further search of tax and land records might help to solve who were the parents of Moses & Nancy.
Instead, I think William & Lidda/Lydia Edwards King moved to Casey County, KY by 1810, where a William King is listed in the 1810 Casey County, KY Census. Lydia's brothers, Isham, Jr. & Hickman Edwards both moved to Casey County, KY, so it seems very possible that the William King in Casey County was the same one who married Lidda Edwards in 1803. William King, age 70 (b. ca. 1780) was still living in the 1850 Census, with a Samuel King, most likely his son. Another King in the 1850 Census was Isham King, who died in 1876, and according to his death record, his parents were William & Lydia King, which seems to indicate that they were the same William and Lidda who married in 1803. Also, the fact that Lydia named her son Isham,suggests he was named for her father.