Shouldn't you be able to get LR for free if you are already paying for PS CC?
There is the $9.99/month deal for both.
I'm not advocating the subscription approach, on the contrary, I argue against it, but if you are already paying for PS on a subscription basis then you shouldn't need to pay extra for LR.
LR-CC+PS-CC for $10/month—Photography Plan.
PS-CC by itself costs $20/month-_Single App Plan.
What are you currently paying for?
Yesterday whenever I looked at Adobe CC on my desktop it showed LR5 ONLY. Tonight it is also showing Lightroom CC 2015 with an Install button. Prior to that it always took me to the Adobe site and the $10/month charge so I kept backing out. I'm downloading it as I write this. I'll see what happens.
So you have PS+LR and were waiting for LR6 to show up. Usually you have to logout using Gear / Preferences / Account / Sign Out, then sign back in.