Pb + Mg(NO₃)₂ → Pb(NO₃)₂ + Mg
This reaction would NOT occur because Pb is less reactive than Mg and as such Pb cannot displace the Mg in order for the reaction to occur under normal conditions.
Mg + Fe(NO₃)₂ → Fe + Mg(NO₃)₂
This reaction would occur. This is because Mg is more reactive than Fe and as such can displace it in the reaction, thus allowing the reaction to occur under normal conditions.
Cu + Mg(NO₃)₂ → Cu(NO₃)₂ + Mg
This reaction would NOT occur. Mg is more reactive than Cu, and as such copper cannot displace magnesium in order for the reaction to occur under normal conditions.