I'm posting this in a separate thread because the issue appears to be popping up in several different discussions here. I just completed a lengthy chat session with Adobe customer support (I'm on the east coast of the United States and the reps were in India, I think), and on the third try I finally was connected to someone who was able to diagnose and resolve my problem.
I have a CC subscription and a standalone ("perpetual") Lightroom 6 license because I want to run LR on more than two machines. Unfortunately, Adobe's license-management software isn't up to the task of dealing with an account holder with both types of license; apparently, when Adobe decided to bring the standalone product under license management, they didn't anticipate that some CC customers (at least, non-institutional customers) would need more than the two seats the subscription provides.
The workaround, actually, is simple: you need separate Adobe accounts for your CC and standalone Lightroom licenses. It's easy enough to register a second account. The only complication is that if you have already purchased a standalone license (upgrade or new) while logged into your existing Adobe account, you will need the assistance of a customer support rep to move that license and, in the case of an upgrade license, the license for your qualifying software to the second account.
Unfortunately, the first-line support rep I spoke to didn't know what to do. Nor did the one to whom he escalated my inquiry. The third rep figured it out with a few nudges from me—I had already guessed the workaround, but was hoping there was a clean fix—and he moved my standalone license to a second Adobe account. I'm now running LR on three machines: two under a CC license and the third under a perpetual license.
And, no, I don't think this hiccup is part of a sinister scheme on Adobe's part to make life difficult for perpetual licensees. Just a lapse in planning.