T-Mobile today announced that it's started rolling out the Android 5.1 Lollipop to its Nexus 6.
However, perhaps more interesting than the rollout itself is that the build that T-Mobile lists for its Nexus 6 rollout, LMY47M, appears to be newer than (or at least different from) the 5.1 builds that we've seen so far.
The first Android 5.1 build that we saw roll out to the Nexus 6 was labeled LMY47D. Then, earlier this week, we saw Google post an updated factory image for the device that brought the build number to LMY47E. It's unclear from the changelog what differentiates this build from the others, or whether it will be hitting other Nexus 6 at large. (Google's Nexus Factory Image page still only lists the "D" and "E" builds.) However, it's worth noting that the Nexus 6 shares a SKU across all carriers, so it probably won't matter which build you update to.
In any event, the OTA update, which clocks in at 409MB, should be rolling out to T-Mobile customers now. The update brings Android 5.1 features like device protection to stop a stolen N6 being used after factory reset, along with bug fixes and feature tweaks. T-Mobile's Des Smith also notes that the update enables VoLTE for T-Mo customers on the Nexus 6. Wifi calling is still coming, though not in this update.