Your information matches what I have found. Most of mine is from a book called "Genealogy of the Lyman Family" by Lyman Coleman, published in Albany, NY 1872. The earliest Lyman ancestor given is Thomas Lyman, who was alive in 1275. It also gives a fairly complete pedigree of Elizabeth Lambert, documenting her decent from Hugh Capet, King of France. From Hugh, you can go back to Charlemagne.There is also a message in the Hill's forum that says Richard Lyman can be connected to the Plantagenet Kings of England, but I haven't found the connection yet.