I am hoping that your brother has been in contact with his Lacota tribe.
Here is the rule of the Oglala Lakota/Sioux:
"ARTICLE II - MEMBERSHIP
SECTION 1. The membership of the Oglala Sioux Tribe shall consist as follows:
(a) All persons whose names appear on the official census roll of the Oglala Sioux Tribe of the Pine Ridge Reservation as of April 1, 1935, provided, that correction may be made in the said rolls within five years from the adoption and approval of this constitution by the tribal council subject to the approval of the Secretary of Interior.
(b) All children born to any member of the tribe who is a resident of the reservation at the time of the birth of said children.
SECTION 2. The tribal council shall propose by-laws covering future membership and the adoption of new members."
The difficulty will be in proving the relationship. If it were possible to do, DNA evidence should prove relationship and should be satisfactory to the tribe (however it would be up to them to decide whether to accept that or not).
In order to accomplish the DNA testing, your brother would need to have his DNA compared to that of one of his father's brothers/sisters, or one of his other known family members (preferably one who is also a registered member of the tribe).
If that is not possible, then he will need to figure out what anecdotal evidence the tribe will require in order to accept who his father was. Some tribes accept a "proof of ancestry" given in front of a circuit court judge (similar to the kind of testimony that is done for a probate proceeding when you have to prove who's who to determine who inherits).
Often a genealogy search is required to trace your ancestry back to a registered tribal member. That is not difficult here; instead the difficulty will be in proving up the paternal relationship in a manner satisfactory to the tribe.
It is the tribe that sets their own standards in this regard.
If you have not already looked at it, take a glance at these web pages:
(All by the US Department of Interior, BUREAU OF INDIAN AFFAIRS.)
Good luck to you and your brother!
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