It is possible for the Natives to die and this can happen in a various ways.
They might die of old age, which is inevitable depending on how long one spends on one particular map.
They can also be burned in the wake of vegatation that has caught fire from contact with lava, or through direct contact with lava itself.
It is also possible for the natives to drown. However, this is not an instant affect like that caused by fire. The native may be swept up by water for whatever reason, and if not rescued in time, they will eventually go below the water level and perish.