According to our reactions:
1) Li(s) + O2(g) ==> Li2O(s)
It is a Redox reaction, Li is oxidized and O is reduced. We have here loss and gain of electrons.
2) It is a precipitation reaction because when the PbI2 is formed, it precipitates.
3) This is the reaction of an acid with a base, so it is an acid/base reaction.