The information in Coleman is not accurate. As in so many 19th century New England genealogies, Coleman is excellent for the American data but uncritically accepts English data which is nonsense.
Donald Lines Jacobus, in his article I cited (TAG Vol. 30  pp. 187-190), says only that Henry Lyman (father of Richard the emigrant) was "quite probably son of an earlier Henry and Joan." Jacobus, probably the most distinguished American genealogist of the 20th century, was himself a Lyman descendant.