After trying to help anewer a question posed by someone who's original Mac had broken seemingly irreparably, I wondered whether it was possible to do as I posed above - access backups made by one unworking computer, which were say stored in the cloud, from another copy of Lr on another machine?
If I had two machines, I'd try it myself, but I only have one desktop.
If you download the catalog file from the cloud and place it on your computer, then in Lightroom use File->Open Catalog.
Of course, you'd need to relink the photos on your computer, otherwise you won't see thumbnails and you won't be able to do anything in this downloaded catalog.
Probably unnecessary to say this, but I will anyways - the second copy would have to be the same version or later.