Owners of the Google Play Edition Motorola Moto G should be getting the Android 5.1 Lollipop update as Google has now released the software.
The Android 5.1 Lollipop update has been released as an over the air update for the Moto G Google Play Edition.
The Moto G GPE Android 5.1 update comes with the build number LMY47M and the update is around 171MB in size, the update brings a range of new features as well as some bug fixed to the Moto G Google Play Edition.
You can check to see if the update is available for your Moto G GPE from the settings menu, alternatively you can manually download the update and you can find out more details about this at the link below.
Source Android Police