Answer
Lewis acid: $Zn^{2+}$
Lewis base: $NH_3$
Work Step by Step
$NH_3$ has a free pair of electrons, and when 4 molecules of ammonia react with $Zn^{2+}$, the metal will receive these electrons.
Since $NH_3$ donates a pair of electrons, it is the Lewis base.
Since $Zn^{2+}$ receives pairs of electrons, it is the Lewis acid.