At the moment, it's unclear if this rough time frame applies just for the unlocked version of the 2013 Motorola Moto X, or if carrier-branded versions will get the 5.1 Lollipop at about the same time.
The original Motorola Moto X was launched back in 2013 with Android 4.2 Jelly Bean on board, but was since updated all the way up to Android 4.4 KitKat. Motorola previously announced that the first-generation Motorola Moto X will be updated straight to Android 5.1 Lollipop, skipping past the 5.0 version of the OS.
At the surface, the most notable changes that Android 5.1 Lollipop brings to the 2013 Moto X include a new Material Design user interface, a new multitasking screen, as well as lockscreen notifications. Under the hood, the update will come with the new 64-bit ART compiler, a new Battery Saving mode, as well as a range of performance improvements and bug fixes. For a full changelist, check out this previous article.
source: David Schuster