EC firmware updates
EC firmware is usually not on the main boot flash and usually could only be changed with the vendor’s tool (running from the vendor boot firmware and usually only on Windows).
It is recommended that you update to the latest EC firmware version. Updating the EC can sometimes provide benefit depending on the vendor. For example, they might fix power issues that could then enhance battery life.
ThinkPads
See the BIOS update without optical disk ThinkWiki page.
Otherwise, check the Lenovo website to find the update utility for your motherboard.
HP EliteBooks
EC firmware is required in the main boot flash, but Libreboot’s build system automatically downloads this from HP for each machine, and inserts it, so you don’t have to worry. Just make sure that vendor files are inserted if using release images.