William's sister, Rosannah WOODS (born 31 Dec 1779 Washington Co., E. TN - died 27 May 1831 Madison Co., AL) married William LAMKIN, Jr. in 1798. More than likely, this was the LAMPKIN/LAMKINs being referred to in Michael WOODS' diary. They are my 4G grandparents.
In 1802 this LAMKIN family was in Roane Co., TN. By 1815, this LAMKIN family had moved to Madison Co., AL. (If William moved with them, you might try either one of those places for marriage/death records of him.)
Hope this helps some. Keep me posted on what you find, I'm greatly interested.