There is a book that give the whole tree of Richard Lyman called Genealogy of the Lyman family in Great Britain & America written in 1872.
Here is the URL for the chapter on Richard:
https://archive.org/stream/genealogyoflyman00cole#page/n84/m...I have used the book to create a full tree up Richards tree on the free website wikitree:
here is the URL for Richard's profile:
http://www.wikitree.com/wiki/Lyman-8.
I have added all the source material that I can find for his ancestors from the book and other places, like the Cambridge alumni website, and the British History online records site.
If you descend from Richard please add yourself and your direct line to wikitree and link up to Richard's tree. This site is collaborative and there is only supposed to be one profile for each person and any new person can link your tree to existing profiles there to build one tree.