I don't have anything that is 100% proven but I do have interesting coincidences.
1) Samuel and Elizabeth named their 2nd son Ichabod, 1st son was Samuel.
2) Ichabod Smith moved from Hadley, MA to Suffield, CT abt 1699.
3) Samuel Lyman m. in Suffield 1723 to Elizabeth Smith. This would make Elizabeth b. abt 1703 if she was about 20 at time of marriage.
4) Ichabod's children were born in Hadley from 1693-1698, the next child born in Suffield in 1700.No other children were recorded until 1708, leaving plenty of space for other unrecorded births.BTW-only 4 births were recorded for this family in Suffield, all boys, 1700, 1708, 1711, 1717.
5) South Street Cemetery records of Coventry, CT lists Elisabeth Lyman spouse of Samuel as d. 28 Feb 1751 age 48 making birth about 1703.Samuel is also there.Nice story about his tombstone.
6) I have photocopies of the film of Icabod's family's vitals, original records.Very poor quality, Elizabeth is not listed, only the 4 boys all at once, Samuel, Ichabod, James, and Joseph.Notice Samuel and Elizabeth's children: Samuel, Ichabod, James, and daughters Elizabeth, Eunice, Desiah, and Dorcas all 8 in birth order.
Like I said, nothing conclusive but a lot of coincidences.And with the name Ichabod in both families, hmmm.Let me know what you think or if I can help further.