There are no separate docs for LE, just have a look at the official RPi docs linked here GitHub - raspberrypi/rpi-eeprom: Installation scripts and binaries for the closed sourced Raspberry Pi 4 EEPROMs - there's also a ton of threads about how to use rpi-eeprom-update / rpi-eeprom-config on the RPi forums (or just call these scripts without parameters and you'll get the usage info).
Only difference on LE is that you don't need to run these programs with sudo as you're already logged in as root.
BTW: probably the easiest way to get the latest eeprom / VL805 firmwares is to boot the eeprom recovery image from SD card - this'll give you the Sep 03 bootloader version as well. Either use RPi imager on your PC or the recovery image from here Release rpi-boot-eeprom-recovery-2020-09-03-vl805-000138a1 · raspberrypi/rpi-eeprom · GitHub
so long,
Hias