Here is what I have recently found on this family. The Lina in 1900 might be your Elizabeth (note the birth date that matches that of Elizabeth).
I have also asked an OBIT-L volunteer in Idaho to try and locate Elizabeth's obit for any information it might contain--
Source: 1870 Census of Nodaway County, MO (Green Twp, PO: Maryville) 285/275 Terhune, George A. 27MW Farmer IN Terhune, Mariah 23FW Keeping house IN Terhune, Marietta 3FW MO
Source: 1880 Census of Nodaway County, MO (Greene Twp, Dist 259) 153/158 Terhune, George A. WM35 Head Married Farmer IN/KY/KY Terhune, Marie V. WF33 Wife Married Keeping house KY/KY/KY Terhune, S?tta WF13 Dau Single Goes to school MO/IN/KY Terhune, Mytie B. WF7 Dau Single Goes to school MO/IN/KY Terhune, Oliver WM4 Son Single MO/IN/KY Duffy, John E. WM16 Neph Single Goes to school MO/KY/IN
Source: www.nebraskahistory.org (Christmas on a Sherman County Homestead, 1884) Amos Edwin Donnell, Sherman County homesteader, left a record of his activities between 1884 and 1888 in the form of letters written to his parents in Missouri.... Among other topics, he reports on...his marriage in 1885 to Ettie Terhune, a Sherman County neighbor.
Source: 1880 Census of Nodaway County, MO (Maryville, Dist 260) 68/74 Terhune, Adam WM63 Head Married Bridge contractor KY/KY/KY Terhune, Elizabeth WF63 Wife Married Housekeeper OH/OH/NC
Source: 1900 Census of Sherman County, NE (Washington, Dist 188) 47/47 Terhune, George Head WM57 Apr 1843 Marr 33 yrs IN/KY/KY Terhune, Marie V. Wife WF53 Feb 1847 Marr 33 yrs 7/9 ch KY/KY/KY Terhune, Oliver Son WM24 Feb 1876 Single MO/IN/KY Terhune, Jesse Son WM19 Jan 1881 Single MO/IN/KY Terhune, Edward Son WM17 Feb 1883 Single MO/IN/KY Terhune, Lina Dau WF14 Jul 1885 Single NE/IN/KY Terhune, John M. Son WM12 Oct 1887 Single NE/IN/KY
Source: WWI Draft Registration Cards Oliver Terhune, b. 10 Feb 1876, res. Acadia, Valley County, NE, nearest relative: Anna N. Terhune (wife)