Pretty sure they use a lithium polymer which isn't pyrophoric and not elemental lithium. If you go down the group 1 metals, Li is the least reactive and doesn't really burn in water either. It needs a lot of energy to combust, hence water being a good way of putting it out as it's self-fueling otherwise.
(This post is brought to you by an ex-chemistry student who managed to blow a phone battery up in a pumpkin and completely destroy it. I wouldn't fly in a Li-ion aircraft).