Google has released Android Lollipop 5.1 for Nexus devices. I installed build 5.1.0 (LMY47E) on my Nexus 6. I had to do this manually (as opposed to waiting for Verizon’s OTA update) because I was not running a stock ROM on the phone.
Bear in mind that I was happy with the phone’s functionality using LiquidSmooth, but because modern phones do not have separate CDMA/LTE antennas, I could not use data services (to include my unlimited-data hotspot, which serves as my primary internet connection) and make voice calls simultaneously. This was extremely frustrating given that I spent over 700 dollars on the phone. Hence the motivation for upgrading the OS to Lollipop 5.1, which provides support for VoLTE.
The process is arcane and non-nerds should not undertake it. Even with my vast system administration and programming experience I found it to be somewhat less than straightforward. The update has to be done over a USB debugging connection on a computer that has the Android SDK installed. Everything on the phone will be wiped out in the process (a fact I became aware of after I saw that all my music was gone following the update). Once you’ve completed the update, it’s easy to reinstall TWRP recovery and apply the SuperSU patch to enable root access.
Incidentally, VoLTE has to be enabled through your carrier account (in addition to device-level support), so I went to my Verizon account settings and did just that. For some reason, this resulted in my inability to send or receive voice calls (data continued to work fine). A quick chat with Verizon technical support and the problem was resolved. I believe this issue was related to my phone not being a Verizon device.
At long last, my Nexus 6 is fully functional and has the capacity for simultaneous voice and data. But achieving this level of functionality took entirely too much technical expertise and intervention on my part. Conclusion: the device is great, the software is okay, and the support sucks.