Just about a week after Motorola released update notes for the second version of its Moto E budget handset, it looks like the Lollipop 5.1 update is indeed hitting the airwaves. Multiple posters on XDA have alerted their fellow users that the update (version XT1527, if you're wondering) has reached their phones. Thanks to the Moto E's off-contract nature, it should hit users on all carriers at the same time.
Screenshot credit: XDA user talbe009
According to screenshots posted on the forum, the update is a bit over 250MB in size, which is practically tiny for over-the-air updates these days. (You can thank Motorola's "I Can't Believe It's Not Nexus" software approach - Samsung updates are pushing a gigabyte or more.) Even so, you might want to hit your nearest Wi-Fi hotspot for the sake of convenience or your mobile data limit.
You'll need a stock firmware and an unmodified System partition in order to flash the update - remember, after Lollipop Android OTA updates fail even for rather benign root-level modifications. As always, it may be several days before the update gets to your particular phone, so keep an eye out for a link or upload of the ZIP file if you're not willing to wait.