Google has begun rolling out the Android 5.1 Lollipop update to Moto G Google Play Edition devices.
As you can see in the above image, the update carries the build number LMY47M.
The OTA update is 171 MB in size, and has already begun rolling out. You can manually check for updates to see if the OTA is available for your phone. But if you cannot wait for it, you can update to the latest version manually. Download the OTA directly from this Google link.
Just make sure that your phone is running LRX21Z, before flashing the update.
NOTE: This update is only for the Moto G GPE. Do NOT flash this update on other Moto G variants. Please wait for Motorola to roll out the update for your devices.