I had a few struggles with this update

(LMY47O, 5.0.2 to 5.1), and I even almost gave up, but finally got it installed on my rooted (stock recovery) Wifi tablet. I originally tried to update using fastboot erase-and-flash of the component img files extracted from the full system image, the same way I'd updated from 5.0 to 5.0.1 and then to 5.0.2. No good - I got the four balls bootloop on first try, and several subsequent tries. I could always still get to the bootloader tho, which is nice. Even flashing the full stock 5.1 image didn't solve the problem, and neither did flashing the stock 5.0.2 image, either components or flash-all.
The recovery mode log kept showing a string of errors, like this one: << E:failed to mount /cache >> (and similar).
Anyway, trial and error ... didn't want to hard reset... I learned I could revive my tablet using Wugfresh's NRT tool. At first I had to 'Flash Stock & Unroot' with the 5.0.2 factory image. This brought me back to life, although I lost all my data, even tho I chose the No Wipe option. Not real bothered, really. I did the same thing again with the 5.1 image, but it again softbricked/bootlooped me.
I finally fixed it for real by using the 'Force Flash' mode with 'No Wipe' UN-checked in the Nexus Root Tool ... with the older 5.0.2 image, then after that was fine and dandy, I did the exact same thing again with the 5.1 image. It didn't work the first time, but I tried the whole 2 flashes again, and I now have a tablet with 5.1 running fine and rooted (with CF).