I've intalled LE (instead of Ubuntu).
Kodi is there, it's all great.
I switched it off then on again, still working.
Then tried to lauch it again, but it remained on the "Intel NUC" screen for a while...
I switched off and on again, and this time, the "Failed to read blocks 0x7" is back... 
Hi,
I'm using the LE with Raspberry Pi (2x RPi3B, one RPi4B), I'm just writing the image to SD-card, put in the RPi and working.
So if I understod correctly, you prepaired an USB stick with the LE and installed the LE to the NUC internal SSD (HDD?)?
You successfully started once or more the LE from NUC internal storage, and after that happen the "Failed to read blocks 0x7" issue?
That looks to me as the installtion went OK, and something happen when you (re)start the LE.
Maybe some kind of BIOS or SSD boot issue in case of LE?
Ubuntu use the Grub as boot manager, maybe the LE use something else?
Could be possible to use two USB sticks? One with the LE "Installation kit" and to be install to another?
Maybe could be useful to share more inrmation about your NUC device, like model, processor, RAM, storage (SSD/HDD), if somebody else using same device and have any idea what is happen.