It's been two years since you posted your message and I hope you are at the same address to receive this reply as I think I have some information that may be what you are looking for as, yes, there is a distant connection.The information I have comes from "Genealogy of the Lyman Family in Great Britain and America" by Lyman Coleman, printed 1872.
John Calvin Lyman (second son of Barnabas Lyman) married in 1840 at Esquiring, Ontario, Susannah Kennedy.Susannah died in 1862 and his second wife was Anna Cisbe.The children of John Calvin Lyman and Susannah Kennedy:
Sarah Susannah,B. April 6, 1841 and married Richard Laird July 22, 1858 ClarissaB. March 30, 1850 Gilbert D.B. Sept. 3, 1851 MarthaB. Sept. 4, 1853 Luther W.B. Aug. 18, 1856 Horatio B.B. Aug. 13, 1859