And Ni-Cd batteries can explode, not just catch fire. Almost as 'easily' as LiPo.
FWIW, LiIon and LiPo are really the same type of battery (LiCoO2, Lithium Cobalt), only the casing is different (and typically the performance parameters).
LiFe or lithium iron, really LiFePO4, has a different cathode material which make is 'safer', but, has less performance capability currently than the Li-Ion. And there are others too, in less use currently, that have other cathode materials.
Li-Ion batteries are perfectly safe, IF (and that's a big IF) the charge, discharge, balance and cooling are properly managed. And you mount them so they are not punctured. And, yes, I have had several LiPo batteries go up in smoke on me, due to charging issues and one was a short circuit.
Li-Fe have proven to be more immune to those kinds of issues, but, they can heat up and cause material nearby to catch fire if they are mistreated, kinda like NiMH batteries.