Like others here I had an OTA system update notification after rooting my Yoga 2 830F. Of course it failed, and this was my method of updating successfully, hopefully it may help others, and provide another method to those already described ,with no need to flash ROM.
When I initially had the tethered recovery the first operation I did was to make a nandroid backup before rooting, in case of any problems. I recommend everyone rooting to do this.
To get the OTA installed I first uninstalled all my apps that required root, being sure to restore back to original where they offered the option to do so, not sure if this is really necessary but wanted to try and ensure no system files were left altered. Then I did a full unroot cleanup from inside SuperSU and rebooted.
I got back to a tethered recovery and restored my nandroid backup and rebooted, then I did a factory reset. At this point I ran the OTA on the device and it succeeded.
Going back to a tethered recovery, made another nandroid backup and then rooted again. I can restore back to this nandroid if another OTA comes along that I want to install. Once booted back up I restored apps and data with TB. Then tethered recovery once more and made another nadroid once everything restored.
The nandroids are kept on the external SD card and backed up to pc, just in case.