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Thank you for posting on History Hub!
Unfortunately we are not likely to have records on the information you seek. We contacted our Subject Matter Expert on Native American records. The BIA and the Army usually did not document what life was like for the Lakota or any other tribes. Our Subject Matter Expert suggested that maybe in RG 75, Letters Received (fully digitized) there may be a mention or two of how Lakota life was structured but it would be be quite difficult to locate as it's quite a large series.
We located some secondary sources that may be useful to your research: https://www.sdhspress.com/journal/south-dakota-history-29-3/reservation-akicitas-the-pine-ridge-indian-police-1879-1885/… and http://plainshumanities.unl.edu/encyclopedia/doc/egp.law.022.
We also suggest you reach out to the Indian tribes as well.
Best of luck in your research!