Will a regular dry chemical home extingusher even begin to put out a burning metal fire like a lithium battery?
Here's what little I know. The information is probably out there on the web if someone has time to dig.
Fire needs three things to live: heat, oxidant (air), and fuel. Remove one of these three, and the fire goes out.
Lithium cells don't have metallic lithium (unless they're way overcharged), but they do carry around their own oxidant, so when things go wrong with a cell it'll keep putting out lots of heat and smoke even if you deny it all air.
Dry chemical extinguishers work by smothering a fire, and denying it air...
I suspect that dumping a lot of dry chemical fire extinguisher stuff on and around a burning battery will do you a lot of good -- the battery won't be getting oxygen from the air, which will restrict the amount of energy it can release, and the dry powder will help prevent other things from catching on fire.
I wouldn't empty all or even most of the extinguisher on the battery, though: I'd put some on the battery, and save the rest to protect any exposed flammables that catch on fire because the battery is torching.