Here is what I know in relation to the Lyman family - A group of 52 people from Postdam NY including 4 Lyman brothers and Rev Billious Pond came to Sangamon County in 1832.Cornilius Lyman (father of Cornilius S Lyman the one who was married to Emily Kincaid) was one of the brothers. Rev Billious Pond went back to Camden NY in 1834 and returned with his entire family in 1837 including Marvin Billious Pond and probably his children Rohada, Cynthia, Saran and Billious his wife probably died in NY, on the way to IL or shortly after coming to IL.Marvin was married a second time in 1839.
In: Fifty years in the Northwest With an introduction and appendix containing reminiscences, incidents and notes By W.H.C. Folsom. Ed. by E.E. Edwards. see: http://www.archive.org/stream/fiftyyearsinnort00folsuoft#page/388/mode/2uphttp://www.archive.org/stream/fiftyyearsinnort00folsuoft#page/388/mode/2up a The next data point is that Cornilius Lyman (the father) along with C. S Lyman (the one you are asking about) is in Stillwater in 1846, Also Rhoda Pond is indicated as addopted by the elder Cornilius Lyman.
Cynthia Amanda Pond is who I am related to and is indicated in Stillwater in 1852.
I seem to recall that one of the Cornilius had a tavern/inn in one of the census.