In 2006 you wrote: "I have a letter she [Lorinda] wrote to her sister (my gg grandmother) in 1875....This letter was signed L A Thompson."
So we know Lorinda's middle initial is A.
Minnesota Deaths (Minnesota Historical Society website) THOMPSON, LUCINDA ADELIA Date of Birth:1822 Place of Birth:NY Mother Maiden Name:REDDING Date of Death:08 OCT 1904 County of Death: DOUGLAS, Minnesota Minnesota death certificate# 1904-32-2871
An online family tree says Lucinda died in Osakia County, which must mean Osakis, Douglas County, Minnesota. (There is no Osakia county.) So the death place is correct, the middle initial is correct, and the birth place is correct. It may be that the transcription of "Lucinda" is a misreading of "Lorinda."
Thus Azalia Gilbert's mother's maiden name may have been REDDING.
You can order Lucinda's death certificate from the Minnesota Historical Society. Most often an original will have much more information - and possibly it will name both "Lucinda's" parents.
Below, found on an online family tree, Ancestry.com (sources for this info not noted):
Hiram Thompson born 05 Jan 1800 Saratoga, NY; died 7 Jul 1879 Osakia, MN 1st married Mary Canfield (children James, William, Sarah) 2nd married Laurinda A Gilbert born 1822, married 22 January 1841 in Jackson County, Michigan(children Ada and Mary)
Clearly it's the same family and you might want to write to the family tree creator.
1860 Rochester, Olmsted, Minnesota Hiram Thompson 60 abt 1800 New York, lawyer Mary Thompson 38 abt 1822 New Hampshire Ada Thompson 15 abt 1845 Michigan
1870 Saint Charles, Winona, Minnesota Hiram Thompson 70 born about 1800 New York, farmer, retired Lorinda or Lucinda 48, born about 1822 in NY, keeping house