The first question that comes to mind, of course, is “can they legally do this under the treaties they have established.” To answer that with any level of competence, I’d actually need to see the treaties in question and particularly the part about withdrawal from same (if there are specific procedures that must be followed or requirements fulfilled, et cetera). The Lakota are completely right about their argument that Article VI of the Constitution demands that treaties entered into by the United States government are binding law upon the United States government, for what that’s worth, but that only goes so far as the treaty. That having been said, I’d find it likely that the Lakota A) have their own lawyers who probably know a lot more about Indian law than I do, and B) are legally confident of their position for a number of reasons.
The second question that comes to mind is “okay, now what?” Can the United States allow – law or not – what essentially amounts to its own version of Taiwan within its borders? And how much land is exactly at stake? I’ve heard people suggest that Lakota territory, under the terms of those treaties from which the Lakota just seceded, stretches as far as the Canadian border. (Not that this helps them much right now, because Stephen Harper won’t do anything to endanger his precious “special relationship” with the biggest dipshit in American presidential history, but I’m sure even with that caveat the Lakota would prefer to not be an entirely surrounded nation like Lesotho or the Vatican.)
Also: be prepared for a shitstorm of indignation considering that Venezuela is one of the nations the Lakota initially approached for diplomatic purposes.
As I said in the post title – this is one of the most significant developments in American political history to come down the pike in a very long time, and potentially one of the most dramatic changes as well – or one of the quickest enforcements of the status quo.