Google is slowly rolling out the Screen Casting support to a few new devices, like the LG G Pad 8.3 Google Play Edition and the Nvidia Shield Tablet. The rollout is very slow and many famous devices haven’t received support for this feature just yet.
Keep in mind that you shouldn’t expect ti receive this as some sort of OTA update, but rather as a server-side change. Both devices mentioned above will get a new tile in the quick settings area, associated to screen casting and you can also use the Chromecast app for the same function. People have already tested the function and claim it works without flaw, at least on the Nvidia Shield Tablet.
The reason for the delayed rollout is unknown, but I must mention that the Shield Tablet also got Android 5.0 Lollipop over the past few days. In the meantime I see people complaining about lack of screen casting support on their Nexus 7 2012 devices, so maybe Google will also do something about that. Apparently, the slow rollout has to do with the fact the service is kind of still in beta phase…