Well I see the problem.
A Louisa Hills d/o Elijah and Mary was born in Glastonbury 15 Nov 1806. ["Connecticut, Vital Records, Prior to 1850," database, FamilySearch (https://familysearch.org/ark:/61903/3:1:3Q9M-CSKJ-SSKX-Y?cc=2843390 : 14 April 2022), > image 1 of 1; compiled by Lucius A. and Lucius B. Barbour, housed at State Library, Hartford, Connecticut.]. The alleged father Elijah died in Glastonbury in 1814. He does not appear to have left a will. It wouldn't do any good anyway because his children would have been minors and Louisa would not have been married yet.
And a Louise Grace Hill born in New Haven 10 June 1806, d. 13 July 1852 in New Haven, married Lewis Fitch 20 Aug 1826. [Society of Colonial Wars in Massachusetts Membership Applications, 1560-1970. (Online database: AmericanAncestors.org, New England Historic Genealogical Society, 2018). https://www.americanancestors.org/DB2755/i/58221/952-co2/1427021068 ]. Unfortunately the application does not list her parents. Her birth, marriage and/or death is not listed in the New Haven vital records. https://archive.org/details/vitalrecordsofne02orde/page/1160/mode/2up
In the CONNECTICUT COURANT, Monday, Aug 28, 1826
Hartford, CT, Vol: LXII, Issue: 3214, Page: 3 "At New Haven, Mr. Lewis Fitch of Norwalk married Miss Grace L. Hill .
I don't see a birth record for Grace Hill either in New Haven or the Barbour Collection.
I suspect that this is a case of Genealogy hates a vacumn. Because no one could find a birth for Louisa Grace Hill in New Haven they latched onto the 1806 birth in Glastonbury. My gut feeling is that she is not the d/o Elijah.
By the way Lewis has a Wikitree profile https://www.wikitree.com/wiki/Fitch-3885
Lewis and Louisa G spent some time in Macon Georgia.