I may have a lead on Joseph Lowery Alexander, although he is not in any part of my Alexander line that I have traced.
My wife's some-multiple grandfather was Joseph Lowery Dysart, born 13 Nov 1817, son of Samuel Dysart, born about 1792, and Nancy Alexander, born about 1796. Samuel and Nancy married in Burke County, NC, and, in 1820, they lived there near Joseph Alexander, who was over 45 years old and may have been Nancy's father or older brother. Joseph Alexander (this one?) married Jane Ussery 13 Dec 1809 in Burke County, NC with Robert Patton as bondsman, and Robert Patton was a son of Samuel Dysart's sister Elizabeth.
The part of Burke County in which they lived became McDowell County.
If the time fits generally, and you are interested, I am willing to cooperate in some research (which I may do anyhow).