It looks like both versions of the Moto X (1st gen and 2nd gen) could soon have the 5.1 version of Lollipop. A soak test for Android 5.1 just started rolling out to some of the folks who own these devices. Here's the quote from David Schuster's Google+ page with the details,
Here is an update for Moto X 1st and 2nd Gen Lollipop 5.1 upgrades.
We started soak test today for Moto X (2nd Gen) for the following retail channels:
Australia, Belgium, Denmark, Greece, Hong Kong, Indonesia, Italy, Malaysia, Netherlands, New Zealand, Norway, Philippines, Poland, Singapore and Sweden
We started soak test today for Moto X (1st Gen) for the following retail channels:
Belgium, Italy, Netherlands, Spain, Australia, Hong Kong, India, Kuwait, Malaysia, Oman, Qatar, Saudi Arabia, Singapore and United Arab Emirates.
If all goes well we would expect full deployments to start next week.
It won't be long now for folks with the Moto X. Of course, even after the soak test there will still be some additional testing for the various carriers, so its still might be a few weeks before it comes to your device.