The original poster is incorrect. The correct way to handle lithium ion battery fires is to put tons of water on them to keep them cool. Most of what's burning in lithium ion battery fires is the electrolyte being heated up by shorting batteries. You want to keep them cool so the electrolyte can't burn.

I would say that using lot of liquid CO2 must cool down a lithium fire while also denying it oxygen to continue. That's what a CO2 fire extinguisher does; it's often used to put out small fires in powered electrical installations.

At a car battery scale, especially in a garage, that would require the use of oxygen masks, and evacuating anyone around, because there won't be much to breathe. Also, of course, the fire truck must carry a large amount of liquid or solid CO2 ("dry ice").

Using liquid nitrogen would be even more efficient, but even harder to provide at scale. Liquid nitrogen is cheap, but cryogenic facilities are not.

The battery contains more than just lithium - It has to be able to sustain a redox reaction internally to do its job.

Fires in lithium ion batteries break down cathode material and release O2 and other combustible gases, as well.

Batteries carry their own oxidizer. You can only cool them down. I also wouldn't be surprised if Lithium reacted with CO2, I know Magnesium does.

Lithium by weight is very little of what's in the batteries. It's not Lithium that's burning. Primarily what's burning in lithium ion battery fires is the volatile electrolyte.