Google released factory images of latest Android 5.1.1 for the WI-FI variants of both 2012 and 2013 Nexus 7. Build number of the update is LMY47V. Both Nexus 7 are not the only devices for which Google released factory images, Google released factory images for Nexus 10 and Nexus player as well.
Latest Android 5.1.1 update doesn't bring any changes like last Android 5.1 update. This update is mainly focused on performance improvements and bug fixes. If you don’t want to wait for OTA, you can grab the latest update factory images by clicking the source link below.
Although Google recently updates its nearly entire Nexus line-up tablets with the latest Android 5.1.0 update but it seems Google software developers are keen to
provide the latest bug fixes to Nexus tablet users.
By looking on Google releasing factory images pattern, we can claim that Nexus 7 mobile data variant Android 5.1.1 factory images will be released in near future. We also have news that Google started rolling out Android 5.1.1 for the Nexus 10, so we can expect Android 5.1.1 OTA roll out for the other aforementioned Nexus tab in coming days.
Interestingly, Google is updating Nexus 10 with the latest Android 5.1.1, A device which was announced couple of years ago whereas the latest Nexus 9 both LTE and WI-FI variants are still on Android 5.0.1.