Lydia was born in 1756. Lydia Rice ... She passed away in 1835.
Sources
Ancestry.com. Massachusetts, U.S., Town and Vital Records, 1620-1988 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2011. Verifies birth on 29 Apr 1862, birth place in Mendon, Massachusetts and parents, Asael and Mary Rice.
Ancestry.com. North America, Family Histories, 1500-2000 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2016. Book Title: Lineage Book of the Charter Members of the DAR Vol 015. Verifies husband as Daniel Greenough.
Ancestry.com. Vermont, U.S., Vital Records, 1720-1908 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2013. Verifies birth in 1762 and death in 1832 in Vermont.
Find a Grave, database and images (https://www.findagrave.com/memorial/58771224/lydia-greeno : accessed 17 February 2022), memorial page for Lydia Rice Greeno (1762–1832), Find a Grave Memorial ID 58771224, citing Evergreen Cemetery, Rutland, Rutland County, Vermont, USA ; Maintained by Jen Snoots (contributor 4661415).
"Massachusetts, Town Clerk, Vital and Town Records, 1626-2001," database with images, FamilySearch
(https://www.familysearch.org/ark:/61903/1:1:Q29P-MRW3 : 20 May 2022), Lydia Rice, 29 Apr 1762; citing Birth, Mendon, Worcester, Massachusetts Bay Colony, British Colonial America, Massachusetts Secretary of the Commonwealth, Boston; FHL microfilm 007011111.
(https://www.familysearch.org/ark:/61903/1:1:FHWC-56J : 20 May 2022), Lydia Rice in entry for Joneas Sibley, 29 Jan 1785; citing Marriage, Sutton, Worcester, Massachusetts, United States, Massachusetts Secretary of the Commonwealth, Boston; FHL microfilm 007009440.
(https://www.familysearch.org/ark:/61903/1:1:FHFF-5B4 : 20 May 2022), Lydia Sibley, 27 Dec 1837; citing Death, Sutton, Worcester, Massachusetts, United States, Massachusetts Secretary of the Commonwealth, Boston; FHL microfilm 007009440.
Find a Grave, database and images (https://www.findagrave.com/memorial/6958256/lydia-sibley : accessed 15 July 2022), memorial page for Lydia Rice Sibley (29 Apr 1762–27 Dec 1837), Find A Grave: Memorial #6958256, citing Sutton Center Cemetery, Sutton, Worcester County, Massachusetts, USA ; Maintained by Ross Weaver (contributor 48435494) .
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Compare to Find a Grave, database and images (https://www.findagrave.com/memorial/6958256/lydia-sibley : accessed 15 July 2022), memorial page for Lydia Rice Sibley (29 Apr 1762–27 Dec 1837), Find a Grave Memorial ID 6958256, citing Sutton Center Cemetery, Sutton, Worcester County, Massachusetts, USA ; Maintained by Ross Weaver (contributor 48435494) .
and https://www.familysearch.org/tree/person/details/LHD9-WK1
Are you sure she didn't marry https://www.wikitree.com/wiki/Sibley-2902 ?