My brother built an electric bike using cheap lithium batteries he bought online. The guide he followed said the system was smart and safe, with no need to worry or really understand how it worked. One night, the bike caught fire in our garage. Lithium fires burn fast and hot, and you cannot put them out with water. By the time firefighters arrived, the garage was destroyed and part of the house was burning. My brother got third-degree burns trying to pull the bike outside.
Lithium ion batteries do not cause lithium fires. If that was the case you should be concerned about the several pounds of sodium that's sitting in your kitchen right now.
Lithium ion batteries have several weaknesses - and they catch fire not from lithium ions, but the stored energy which creates an internal short circuit that rapidly generates a lot of heat. Couple that with flammable electrolyte and cell materials that contains oxidizers and you get the recipe for a fire. The lithium itself is fairly stable in its ionic form and it's very reluctant to replace the lost electron.
It's not the lithium - because if you take a discharged battery and a charged battery and puncture them, the discharged battery (or really, anything below 50% charge) will at best spew a little contents out. meanwhile the charged battery produces exciting fireworks.
Lithium primary cells though do contain actual metallic lithium and are exciting, but their expense and non-rechargeable nature mean they are not very prevalent.
As for your kitchen - sodium in the form of table salt. Sodium chloride, which has both the reactive sodium metal plus the poisonous gas chlorine, but together is rather innocuous other than giving you high blood pressure.
If you have dodgy cells, if you're willing to give up half their capacity, they will not cause a fire even when damaged as at 50% they do not have enough energy stored to discharge with flame.