At this time there are no functions built into the camera that will support firmware for non-Canon lenses. I apologize for any inconvenience that this may cause you.
"Can I update firmware ..."
No Canon lens, I know of, is user FW updateable. What exactly is the problem that makes you think it isn't working right?
I don't think that's true, Ernie. Canon has added lens firmware update capability to some of their higher-end cameras (maybe even your 1DX2!), and I doubt they'd have done that if none of their lenses could be updated.
If that is a possibility I still have to repeat my original statement, "No Canon lens, I know of, is user FW updateable."
It would almost certainly have to be a newer lens than I have. Perhaps the 70-200mil model 3.
Some of the most recently released lenses can be upgraded by the user by using the camera.
That is an announcement for a firmware update for a couple of EF-M series lenses. Many of the “great whites” can be upgraded by the user, too. Other lens manufacturers offer the feature, so I cannot see Canon not following suit.
09/26/2023: New firmware updates are available.
08/18/2023: Canon EOS R5 C training series is released.
07/31/2023: New firmware updates are available.
05/31/2023: New firmware updates are available.
05/18/2023: New firmware updates are available.
03/30/2023: New firmware updates are available.