Jemima was born in late 1845 in Witney, Oxfordshire, England.  She was the daughter of Richard Lardner and Emma Tomkins. Her parents were married roughly a year before her birth.  Her father died in 1848.  Her mother was remarried the following year to Joseph Gould. 
Jemima appears as a daughter in the household of Emma and Joseph in the 1851 Census.  She was five years old at the time. Jemima emigrated with her family to the United States on the ship James Nesmith, which departed from Liverpool and arrived at the Port of New York, 19 Sep 1853.  The family settled in Elgin, Illinois by the time of the 1860 US Census, at which time she was 15 years old. 
Although her mother appears on the 1860 records, the obituary of her step father places her mother's death in 1860. Joseph remarried before the end of 1860.  Joseph's new wife gave birth in early 1862. In August of that year, Joseph was inducted into Union Infantry and went off to fight in the US Civil War. He returned in 1865 in very poor health. It's not clear when Jemima left home, but her subsequent life is unknown. Jemima has not yet been found to appear in the records of the United States or the United Kingdom.
This suggests two reasonable theories. The first is that she returned to the United Kingdom, but not to Oxfordshire. There are any number of records for Jemima Lardner, or even Jemima Gould from British sources, but these are not clearly attributable to the person of this profile. The second theory is that she remained in the United States or Canada, but did not remain in Illinois or go to Wisconsin. Again the problem is attribution. The facts of her life after 1860 are unclear and the time and place of her death are unknown.
↑ "England and Wales Birth Registration Index, 1837-2008," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:26PJ-1SB : 1 October 2014), Jemima Lardner, 1845; from "England & Wales Births, 1837-2006," database, findmypast (http://www.findmypast.com : 2012); citing Birth Registration, Witney, Oxfordshire, England, citing General Register Office, Southport, England.
↑ Oxfordshire, England, Church of England Marriages and Banns, 1754-1930. Oxfordshire Family History Society; Oxford, Oxfordshire, England; Anglican Parish Registers; Reference Number: BOD203_c_6. Ancestry.com. Lehi, UT, USA: Ancestry.com Operations, Inc. 2016. Output: Name: Emma Tomkins; Gender: Female; Date: 25 Dec 1844; Marriage Place: Oxford, St Giles, Oxfordshire, England; Spouse: Richard Lardner.
↑ "England and Wales Death Registration Index 1837-2007," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:2J97-RVM : 31 December 2014), Richard Lardner, 1848; from "England & Wales Deaths, 1837-2006," database, findmypast (http://www.findmypast.com : 2012); citing Death, Chipping Norton, Oxfordshire, England, General Register Office, Southport, England.
↑ "England Marriages, 1538–1973 ," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:N2DM-599 : 10 February 2018), Joseph Gould and Emma Lardner, 12 Mar 1849; citing Saint Giles,Oxford,Oxford,England, reference , index based upon data collected by the Genealogical Society of Utah, Salt Lake City; FHL microfilm 887,487.
↑ "England and Wales Census, 1851," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:SGXS-2HD : 24 October 2017), Jemima Lardner in household of Joseph Gould, Ducklington, Oxfordshire, England; citing Ducklington, Oxfordshire, England, p. 2, from "1851 England, Scotland and Wales census," database and images, findmypast (http://www.findmypast.com : n.d.); citing PRO HO 107, The National Archives of the UK, Kew, Surrey.
↑ "New York Passenger Lists, 1820-1891," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:2752-HHP : 11 March 2018), Emma Gould, 1853; citing NARA microfilm publication M237 (Washington, D.C.: National Archives and Records Administration, n.d.); FHL microfilm. From Image: Ship: James Nesmith; Departure: Liverpool; Arrival: New York, 19 Sep 1853. Gemima Gould shown as age 7, accompanied by Emma Gould.
↑ "England Marriages, 1538–1973 ," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:N2DM-59S : 10 February 2018), Joseph Gould and Emma Lardner, 12 Mar 1849; citing Saint Giles,Oxford,Oxford,England, reference , index based upon data collected by the Genealogical Society of Utah, Salt Lake City; FHL microfilm 887,487.