I am a descendant of Governor Sevier Lawson, the oldest son of Joshua and Telitha Lawson. Please look at my tree for the information on their descendants. I have recently been DNA tested through the Lawson DNA Project and have confirmed that Joshua and the Lawson family of Greene County, IL descended from the Lawson family of Falling River, Virginia. We are still trying to verify just how Joshua relates to the Falling River Lawsons.
I think Joshua was the son of John Lawson and Anna Lawson (his first cousin). John was probably the son of Bartholomew Lawson and Susannah Simpkins, the grandson of William Lawson and Isabella Kenny, and the great-grandson of Joshua Lawson and Ann Smith. But none of this is yet verified.
information on Bartholomew:http://www.lawsondna.org/Pages/Bartholomew1timeline.html
information on William: http://www.lawsondna.org/Pages/William1timeline.html