I have a keen interest in both the Lane and Thompson families, so your question fascinates me. My Lane ancestors are originally from Tioga County, but settled in Onondaga County. The Thompsons in western Onondaga County were church planters themselves. I will certainly look into this. Is this the same Rev. Lane?
From 1811 to 1819 this people were supplied with monthly missionary preaching, and worshiped with the Aurelius society, who then occupied the old stone church, which stood opposite the place now owned by Dr. Hamilton. Occasionally, however, services were held in the old school-house in Cayuga, by Rev. Joshua Lane, Revs. David Smith and Mr. Sullivan. Home Missionaries from Connecticut, also labored here during that period, the latter about one year. The Presbyterian Church of Cayuga, was organized May 3d, 1819, in the school-house which forms the rear part of Davis' Hall, a preliminary meeting being held for that purpose at the same place April 26th, 1819. The members constituting the society were John Fitch, Gershom B. Gillett, Loring Willard, Jeremiah Hallock, Bezaleel Shaw, Jr., Abbey P. Allen, Percy Shaw, Temperance Beman, Susan Annin, Meliscent Foot, Roxy Ann Foot, Parthenia M. Foot, Philomela Perry, Polly Savage and Tabitha McIntosh, members of the church of Aurelius. Loring Willard, Jonathan Whitney, Uri Foot, Daniel McIntosh, Solomon Dewey and Jeremiah Hallock were elected trustees. The meeting at which the organization was effected was attended by Revs. Joshua Lane of the Presbytery of Cayuga, and Wm. Bacon of the Presbytery of Geneva. On the 20th of June following, twelve more were received by letter from the Church of Aurelius, and Thomas Mumford, Jeremiah Hallock, Elias Thompson and Gershom B. Gillett were elected ruling elders, and Elias Thompson was chosen deacon.