Nothing special should be necessary if your RPi 4B does not have a very obsolete bootloader.
Just write a LE image to your external SSD, connect it to RPi 4B and try to boot.
if it won't work, try the same with SD card ( this should definitely work ), then check the VL805 USB firmware & RPi bootloader versions and upgrade them to latest available (check the release notes here).
How to check the CURRENT versions: rpi-eeprom-update
VL805 release should be: 00138a1
BOOTLOADER should be: Thu Apr 29 16:11:25 UTC 2021 (1619712685) or later.
You may easily upgrade the VL805 USB firmware & RPi bootloader (not to latest available but to versions contained in LE but useable) from Kodi: Settings - Libreelec - Updates - Firmware Updates
Usually the VL805 USB firmware is already at the latest available version (00138a1) but the bootloader is a bit obsolete.
This way you may upgrade it from SSH console to (currently latest) release 2021-04-29 (and the VL805 as well, if it's not the 00138a1 yet):
cd /tmp
wget -c https://github.com/raspberrypi/rpi-eeprom/releases/download/v2021.04.29-138a1/rpi-boot-eeprom-recovery-2021-04-29-vl805-000138a1.zip
unzip rpi-boot-eeprom-recovery-2021-04-29-vl805-000138a1.zip
rpi-eeprom-config pieeprom.bin > bootconfDefault.txt
# default config
echo Default config:
cat bootconfDefault.txt
vcgencmd bootloader_config > bootconf.txt
# current config
echo Current config:
cat bootconf.txt
rpi-eeprom-config /tmp/pieeprom.bin --config /tmp/bootconf.txt --out /tmp/pieeprom
rpi-eeprom-update -d -f /tmp/pieeprom
# VL805 USB firmware upgrade
rpi-eeprom-update -u /tmp/vl805.bin
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Then you may try to boot from external SSD again. If it still won't work (test on both USB3/USB2 ports), check if the power from USB port is sufficient for your SSD (test with USB hub with external power supply or with a fork USB cable).
The last thing to be done when you make the LE booting from external SSD is to add this line to /flash/config.txt file in LE:
dtparam=sd_poll_once=on
otherwise there was a repeating error message filling log due to missing SD card (not sure if it's still necessary).
mount -o remount,rw /flash
echo dtparam=sd_poll_once=on >> /flash/config.txt
mount -o remount,ro /flash
Hope this helps.
Edit: 2021-05-01 - updated link to current firmware above.
Edit: 2023-01-15 - added update scripts for most current releases below.
# RPi 4B - USB controller upgrade:
cd /tmp
wget -O USBfirmware.bin -c https://github.com/raspberrypi/rpi-eeprom/raw/master/firmware/stable/vl805-000138c0.bin
rpi-eeprom-update -u USBfirmware.bin
reboot
#
# RPi 4B - Bootloader upgrade:
cd /tmp
wget -O pieeprom.bin -c https://github.com/raspberrypi/rpi-eeprom/raw/master/firmware/stable/pieeprom-2023-01-11.bin
rpi-eeprom-config pieeprom.bin > bootconfDefault.txt
cat bootconfDefault.txt
vcgencmd bootloader_config > bootconf.txt
cat bootconf.txt
#nano bootconf.txt
rpi-eeprom-config /tmp/pieeprom.bin --config /tmp/bootconf.txt --out /tmp/pieeprom
rpi-eeprom-update -d -f /tmp/pieeprom
reboot
#
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