I'm betting she's the Lucy MITCHELL who appears on the same census page as Jesse LANCASTER and his family in the 1900 census.They are 4 households away: MITCHELL, Mary b. Dec 1840 in AR, widowed, 13 children born, 5 children living, both parents b. IL dau Susan J. b. Feb 1869 in AR, father b. MO, mother b. AR dau Martha b. Apr 1872 dau Elizabeth b. May 1877 dau Lucy b. Nov 1881
The 1880 census for Beaver, Saline Co, AR: MITCHELL, James F. age 56 b. AR, father b. NC, mother b. TN, farmer wife Mary E. age 30 b. AR dau Susan J. age 11 b. AR son Richard S. age 11 b. AR dau Martha age 7 b. AR son Thomas J. age 5 b. AR dau Elizabeth age 3 b. AR
1870, same location: MITCHEL, James age 46 b. AR, farmer Mary E. age 27 b. AR David age 15 b. AR Susan J. age 1 b. AR Samuel R. age 1 b. AR
In 1870 they were living right next door to the LANCASTER family.
There's a marriage record for James MITCHELL, age 44, to Mary STRICKLING, age 26, on 21-Jun-1868 in Saline Co.