Long story short: to find death and burial of Lise, my advice is:
1) look for Lise Hagen or Haugen (this is iffy, also could be her other name variants)
2) look from about May 1875 to about May 1876
3) look in La Crosse County, Wisconsin
Parents of Lise Iversdatter (Skeggestad) b 18 Aug 1846 were Iver Olsen (Martinbakken) and Kari Simensdatterhttp://www.arkivverket.no/URN:kb_read?idx_kildeid=8939&i
Parents of Kari Simensdatter (Brettingsbakken) b 03 Nov 1805 were Simen Monsen and Lisbet Pedersdatter.
The parents' names might be included in a death record and thus be key in making a definite id.
Marthine lived with her aunt after her mother's death - obit says this was John's sister "Mrs. B. Skogstad."
John's parents were Gunder Olsen and Berte (Birrthe) Jonsdatter (Johnsdatter). All their (known) children except Ole emigrated to America.
Ole Gundersen b 18 Mar 1826 stayed at the farm in Norway
Ingeborg Skjeggestad b 17 Feb 1828
John Skjeggestad b 16 Oct 1833 (Marthine's father)
Johan Skjeggestad b 17 June 1836
I would guess this is Mathia, buried in Lone Rock Cemetery, Flandreau, South Dakota:
Birth: 01 Jan 1840
Death: 08 Jun 1884
So then Mathea's husband is likely Bernt Christianson Skogstad, the only other Skogstad buried at Lone Rock Cemetery:
Birth: Nov 1845
Death: 21 Jul 1902
So then Mathia would be John's sister "Mrs. B. Skogstad" with whom Marthine first lived when her mother died. And then Mathia died when Marthine was only about 14.
So then Marthine's cousin Carl must be
Carl B. Skogstad
Death: 08 Oct 1956
buried at a different cemetery (Union cemetery), but also in Flandreau, Moody, South Dakota
along with his wife Chloa Annette.
Searching Find-a-Grave for "Skogstad" in Moody County, South Dakota, only these two couples are listed.
Here is a link to a family tree for Bernt Christiansen Skogstad:http://geneastory.com/genealogy/getperson.php?personID=I4189
Father Christian Christiansen Skogstad b 1812
Mother Karen Olsdatter b 1812
1. Kristiane Kristiansdatter b 23 Mar 1838, Vestre Toten, Oppland, Norway d 12 Apr 1906, La Crosse, La Crosse, Wisconsin, USA
2. Ole Christiansen Skogstad b 17 Jan 1841, Land, Oppland, Norway
3. Andreas Christiansen b 03 Feb 1844, Land, Oppland, Norway d 1877, Mower, Minnesota
4. Berndt Christiansen b abt 1846, Søndre Land, Oppland, Norway <----------------------------------
5. Carl Christiansen Skogstad b 03 Jan 1855, Søndre Land, Oppland, Norway d 27 Jun 1926, Frankford Twp, Mower County, Minnesota
The list of Skogstad children above would be the sister-in-law and brothers-in-law of John Skjeggestad's sister Mathea, if we've got this all figured right. If so then little Marthine probably would have known these people.
You can read more about Cal Christiansen Skogstad b 1855 in "History of Mower County" and enjoy the tales of the "Bear Creek Boys." Here's an obit for this Carl (brother to Bernt, not the Carl b 1870 who was son to Bernt):http://www.dalbydata.com/user.php?action=resultobits
Skogstads who are buried at Bear Creek Lutheran Cemetery:http://www.rootsweb.ancestry.com/~mnmower/cems/bearcree.htm
Bernt's sister Kristiane had a daughter Karoline Anderson who died as a baby in 1877 - so, the death occurred only a year or two later than Lise Iversdatter Skjeggestad's death. The creator of the family tree online says he found Karoline's death record "in the records of Our Savior’s Lutheran Church of La Crosse."
That could be a clue as to where to look for the deaths of Lise and Kari (maybe find them or maybe not but worth a look).
Bernt's sister Kristiane is buried at Oak Grove Cemetery, La Crosse, La Crosse County, Wisconsin.
Anyway, at the very least investigating this lead likely will clear up the mystery about who is meant, when it was said that Marthine was sent to the Skogstads. I followed up on this because of the chance that Lise and her mother would be buried in a church cemetery in a church with which the Skogstads were affiliated, perhaps near La Crosse, Wisconsin, before the Skogstads moved to Mower County.
Hope this helps.