GR, don’t confuse “Lithium” batteries with “Lithium-Ion” batteries.
”Lithium” batteries, also known as Lithium Metal batteries are non-rechargeable, generally small, and are not very common on aircraft, although sometimes used by photographers. My Nikon DSLR came packaged with a free one. They are also sold in common sizes as an expensive alternative to Alkaline single-use cells. They are also common as “button” cells for watches etc. They contain lithium metal, which reacts with water. They do not tend to pose a fire risk on aircraft when contained in equipment, although there are risks to carrying them in bulk shipments, and have a significant dangerous goods code accordingly.
”Lithium-Ion” batteries, are the rechargeable ones used in mobile phones, tablets, computers, video cameras and power tools. Sometimes known as Lithium-polymer, or Li-Po. As stated earlier, they contain Lithium compounds, not Lithium metal. The best extinguishing method is to immerse in water - removing heat and preventing any further heat buildup. It is the heat that causes the fire. The heat is caused by the battery self discharging due charging fault or damage. The fire is not burning lithium, it is the flammable organic electrolyte contained within the cell that catches fire. This is why water works very well with this type of battery. As shown in the FAA video posted above, halon/BCF can extinguish the fire, but it does not halt the thermal runaway within, so it is likely the battery will re-ignite if not continually quenched or immersed in water.
I agree that the report you quoted creates confusion. On one hand, the author makes the distinction between lithium and lithium-ion batteries, but then goes on to not appear to understand the difference when it comes to fire extinguishing. Hopefully we are now better informed 8 years down the track.