By attacking the settlers and trying to remove them from land they claimed was Lakota territory, the Indians were attempting to reassert sovereignty over a fixed piece of territory, which is an action historically and traditional associated with a nation state. They had already given up that status by agreeing to treaties with the federal government. In addition to giving up control over the land, the Lakota had also decided to become wards of the state and recipients of payments of money, food, etc. Everything, even disputes about the basic fairness of the treaty or the mismanagement of the payments fell under federal government and court administration. In addition, at the time of the Lakota War, Minnesota had been admitted to the Union as a state. This meant that they were subject to Minnesota law as well as federal law and the treaties they had agreed to.
The war resulted in defeat for the Lakota. So their attempt to throw off U.S. sovereignty had failed. Consequently, once voluntarily and once by force, the Lakota had been compelled to acknowledge the sovereignty of the United States over the disputed territory.
The Lakota claim to that territory was extinguished by the treaties they signed and that extinction was further reinforced when they broke the treaty by resorting to unrestricted warfare. In doing that, they became a gang of common criminals punishable under Minnesota and Federal law.
Lincoln guided the sword of justice pretty carefully. He ultimately approved death sentences only for those defendants his review team felt had been proven guilty of committing actual civil crimes (murder, rape, etc.). For those who had simply rebelled and participated in battles, he commuted their death sentences to prison terms.
This parsing into discrete groups was indicative of his approach to the Civil War.
If you read his speech to Congress after the attack on Fort Sumter, there is a subtext of checking off the procedural boxes when communicating with South Carolina’s governor just like he was still dealing with a state of the Union. South Carolina was going to have to prove by its actions - not angry words - that it really was in rebellion. South Carolina, of course, was glad to oblige.
Ditto for the Emancipation Proclamation: months of notice before it took effect, a pathway for return to the Union while preserving slavery (for a season), and specific exemption for the northern slaveholding states.
Finally, his instructions to Grant and other Union commanders that he did not want harsh measures taken against surrendered Confederate military units, their commanders, or the civilian leadership. Lincoln, of course, was murdered shortly thereafter, but Presidential Reconstruction was less harsh than the period of Congressional Reconstruction that followed. As far as I can recall, the one execution carried out of a notable Confederate official was that of Captain Henry Wirz, CSA, the camp commander of Andersonville prison camp:
https://en.wikipedia.org/wiki/Andersonville_Prison?wprov=sfti1
Wirz was adjudged to have committed actual war crimes - as opposed to have simply been in rebellion. That trial and verdict somewhat mirrors Lincoln’s approach and decision with the Lakota 38.
Well reasoned and backed up with facts.
But the Lakota 38 were people of color, and a disproportionate number of them were Lakota, an oppressed indigenous people. In fact, all of them were. So Red Lives Matter, and Bearded Stovetop Hat Man Bad.