I have found information about Thaddeus Lyman in the book, "Descendants of John Dwight of Dedham, Mass.", by Benjamin W. Dwight Vol I. Published by John F. Trow & Son, Printers and Bookbinders 205-213 East Twelfth Street, New York 1874.
This is only what the book gives. "Thaddeus Lyman, b. March 16, 1746, went to Mississippi,and m., but whom or when or with what issue, if any, no one of his descendants now knows. On the death of his first wife, he returned to Suffield, where he m. about 1784 Apphia Olds."
There is more information of him in Suffield, CT. If you would like to e-mail me, I could tell you more about Thaddeus. Maillady7 @ aol.com
I'm sorry I could not provide Thaddeus' first wife's name.
I have not heard of the well known story of the harrowing trip made by the Lyman group across Indian lands.