Joe bought this guitar around 1975. This is according to Willie’s Guitars shop, through which the guitar went in 2022 before it was sold to Joe Walsh once again. You can read all about this here – 1959 Gibson Les Paul Standard “THE ROCKY MOUNTAIN WAY BURST” by Willie’s Guitars.
As far as when and where Joe used this guitar, in the July 2022 issue of the Vintage Guitar magazine, Joe noted that he thinks that he used it on his live solo album You Can’t Argue with a Sick Mind. This album was recorded before Joe joined the Eagles, which would obviously mean that he had this guitar when he was playing with the Eagles.
Joe had a few Les Paul Standards in the 70s and the 80s, and due to the lack of high-res photos, and the fact that the guitar now faded in color, it’s hard to match it to anything from those years with certainty. However, based on the Vintage Guitar story published in the July 2022 issue, the line of ownership is pretty well established.
Joe Walsh didn’t play this on ‘You can’t argue with a sick mind’, as the concert footage shows him playing a natural, rosewood board Stratocaster for most of the show, and when he switches to a Les Paul for ‘Rocky Mountain Way’, it is a burst conversion with a slanted bridge.
However Glenn Frey plays a Les Paul sunburst in the film this could be the Les Paul in this article and was almost certainty in the Eagles guitar collection. (Don Felder plays a sunburst Stratocaster in the film)