The original cuts don't exist as a film master. Lucas had them destroyed. Only the non-anomorphic 1993 LaserDisc exists as a source and that wasn't good enough for Blu-Ray.
That's not really true. Nor is pretty much everything else posted about this in the last page of this thread about the OT (not just picking on you, LOL - there is a lot of misinformation out there so it's no wonder folks are confused).
1) The O-Neg (which actually ran through the camera) was spliced to make the SE's, this is true. The sad, infuriating part is that the O-Neg (which when they cracked open the cans had deteriorated to such a degree they were not sure it
could even be saved) was completely and thoroughly chemically restored to pristine condition before this happened.
2) He did not "have (it) destroyed" per se, but since digital technology wasn't very far along in the mid-90's to actually scan the entire film to work from, when he was doing this (much the problem with the SE's in general, the tech just wasn't good enough for what he was attempting), he chose to let them be cut up and the SE's were physically assembled from them. One frame on each side of each cut that was made has been lost due to how one must physically cut film.
3) In spite of the state of the O-Neg, with the exception of those missing frames, the cut portions were supposedly saved, meaning it would simply need to be spliced back together again.
4) Even without the O-Neg, Lucasfilm has the original IP's (interpositives) made from it, as well as several existing Technicolor prints and other sources, being easily available. This includes the print that the Library of Congress holds - which they famously would not allow Lucas to remove and replace with the bastardized versions. You can make an appointment at the LoC to view the print yourself, so certainly it could be accessed by Lucasfilm if it really was needed as a last ditch.
5) Lucas really doesn't give a crap anymore. He said as far back as 2010/2011 during the Blu-ray release that it could be done, it just would cost a few million dollars and he wasn't personally interested in doing it. He long ago gave up the rhetoric and hypocritical stances he previously held regarding it. It just wasn't going to be done on his dime.
All that said, there are pretty solid rumors that restoring the OT negatives was literally the first thing that Disney did upon purchasing Lucasfilm back in 2012, while they were figuring out what to do about the future films, using whatever option was best/available, and that it's been done for some time now. It's just a matter of when and how they decide to release them. I think a lot of us expected it to happen before TFA, but they may be saving them for a future box set - who knows.
I'm guessing there is also some discussion over how best to present them - because some work the SE's did (on matte lines, etc., particularly in space) really need to be done for it to look good in HD. Sure, when projected on a big screen the matte lines are more diffused and less apparent, but squeezing HD resolution into the size of a flat-screen TV highlights them tremendously. It's a fine line they will be walking when doing the actual transfer.
So not only is it possible, it's pretty likely already been done - it's just a matter of when Disney/Lucasfilm decides to drop them and how.