In LE 8.0.2 - enter LE settings - set update to manual - set update channel to libreelec-8.0 - check for updates - select 8.1.0 - let it update. This will give you 8.1.0 which will automatically update to 8.1.1 sometime in the next 48h (prob) and eventually to 8.2.0 when released.
LE before 7.0.3 or any OE devices need to do it the old way copying .tar files around.