You're conflating two different battery types. The lithium in lithium-ion batteries is bound to either the cathode or anode, so it's not readily flammable as metallic lithium would be.
I am conflating nothing as I was summarizing the comments of other people in that sentence. The other comments do conflate different battery types; you can educate the people who make them. Ctrl+F "lithium" in this thread will get you plenty.
You're conflating two different battery types. The lithium in lithium-ion batteries is bound to either the cathode or anode, so it's not readily flammable as metallic lithium would be.