  Recently, the authors obtained the Schur multiplier, the non-abelian tensor
square and the non-abelian exterior square of $d$-generator generalized
Heisenberg Lie algebras of rank $ \frac{1}{2}d(d-1).$ Here, we intend to obtain
the same results for $d$-generator generalized Heisenberg Lie algebras of rank
$ t$ when $ \frac{1}{2}d(d-1)-3 \leq t\leq \frac{1}{2}d(d-1)-1.$ Then, as a
result, we give similar consequences for a nilpotent Lie algebra $ L $ of class
two when $ \dim (L/Z(L))=d,$ $ \dim L^2=t $ such that $ \frac{1}{2}d(d-1)-3
\leq t\leq \frac{1}{2}d(d-1)-1.$
