Android Lollipop 5.1 update is in the process of being rolled out for the Moto X and Moto E devices. Regarding the Moto G, there is no official confirmation whether the update will be available to the first and second generation Moto G devices or not.
U.S. Cellular rolled out the Android 5.1 Lollipop update to the 2nd gen Motorola Moto X. It is available for all the subscribers in the OTA format. U.S. Cellular released the Android 5.1 Lollipop update for the Moto E LTE devices also.
AT&T also plans to release the update to their subscribers who have the 2nd generation Moto X very soon. The exact release date of the new update is not yet known.
Currently, the Moto X 2013 smartphones are running on Android KitKat and anxiously waiting for the new update to Android Lollipop. The company does plan to release the Android Lollipop 5.1 update to their patrons.
In this regard they released a statement, which says that, "This device will be upgraded to Android 5 Lollipop release of Android, pending partner support." However, the company did not announce any official date of rolling out the Android Lollipop 5.1 update for Moto X 2013.
Regarding Moto G, there is no official confirmation whether the first and the second-generation devices will get the new Android Lollipop 5.1 update or not. They are currently running on the Android Lollipop 5.0 version.
According to TechDroider there is a slim chance that the update will arrive for the 2nd generation Moto G.The site said that the company was conducting tests on the second-generation Moto G devices. However, in the absence of any conclusive proof, it was taken to be a rumor, according to Gospel Herald.