>Li ... explodes on contact with water ...

Metal, yes, because it energetically liberates the hydrogen from the water which the explosively recombines with oxygen ... sodium METAL does the same thing. Lithium carbonate and similar compounds used in batteries, no. Batteries using Li metal have been built, and have excellent energy storage and power delivery rates, but are short-lived and unstable. The Li in Li-Ion batteries is not in metal form, and in fact plating out as metal (which can occur under certain forms of abuse) destroys the electrode and the battery.

The tendency toward fire comes mainly from the flammable electrolyte used in Li-Co-Al/Mn batteries. If the battery gets too hot, such as from external heat exposure (hence active cooling systems in high-capacity batteries), excessive current taken out of the battery (such as by an external short circuit), or an internal short circuit (there are several ways to develop an internal short), it can go into thermal runaway and heat the electrolyte to the ignition point. Li-Fe-P batteries use a different electrolyte, and are less subject to internal shorts and other things that can cause thermal runaway; in return, they store less energy per unit volume and weight, deliver less power, and are heavier than the chemistries typically used in cars, but are much longer-lived than typical EV batteries. Tesla is switching to LFP batteries for cars built in China due to safety regulations, with a substantial loss of range compared to the same model built in the US.