  In this article, associated with each lattice $T\subseteq \mathbb{Z}^n$ the
concept of a harmonic-counting measure $\nu_T$ on a sphere $S^{n-1}$ is
introduced and it is applied to determine the asymptotic behavior of the
eigenfunctions of the Laplace-Beltrami operator on a lens space. In fact, the
asymptotic behavior of the cardinality of the set of independent eigenfunctions
associated with the elements of $T$ which lie in a cone is determined when $T$
is the lattice of a lens space.
