  We use classical methods from analytic number theory to resolve the lattice
point counting problem on the first Heisenberg group, in the case where the
gauge function is taken to be the Cygan-Kor$\acute{a}$nyi Heisenberg-norm
$\mathcal{N}_{4,1}(z,w)=(|z|^{4}+w^{2})^{1/4}$. In this case, our main theorem
establishes the estimate $\mathcal{E}(x)=\Omega_{\pm}(x^{\frac{1}{2}})$, where
$\mathcal{E}(x)=\mathcal{S}(x)-\frac{\pi^{2}}{2}x$ is the error term arising in
the lattice point counting problem, $\mathcal{S}(x)$ is given by
$$\mathcal{S}(x)=\sum_{0\leq m^2+n^2<\, x}r_2(m)$$ and
$r_2(m)=|\{a,b\in\mathbb{Z}:\,a^{2}+b^{2}=m\}|$ is the familiar sum of squares
function. As a corollary, we deduce that the exponent $\frac{1}{2}$ in the
upper-bound $\left|\mathcal{E}(x)\right|\ll x^{\frac{1}{2}}\log{x}$ obtained by
Garg, Nevo & Taylor can not be improved and is thus best possible, thereby
resolving the lattice point counting problem for the case in hand.
