The brand new Android 5.1.1 (build LMY48G) update for the Nexus 7 (2013) WiFi that first serviced via factory image earlier in the week is now available for download as an over-the-air .zip from Google. Yep, you can sideload this little guy as long as you are coming from LMY47V.
For instructions to sideload using adb, check here. You can download the file through the Google link below.
Download Link [LMY48G from LMY47V, 18MB]