  Let $\mu_1\ge \mu_2\ge\cdots\ge\mu_n$ denote the Laplacian eigenvalues of $G$
with $n$ vertices. The Laplacian-energy-like invariant, denoted by $LEL(G)=
\sum_{i=1}^{n-1}\sqrt{\mu_i}$, is a novel topological index. In this paper, we
show that the Laplacian-energy-like per vertex of various lattices is
independent of the toroidal, cylindrical, and free boundary conditions.
Simultaneously, the explicit asymptotic values of the Laplacian-energy-like in
these lattices are obtained. Moreover, our approach implies that in general the
Laplacian-energy-like per vertex of other lattices is independent of the
boundary conditions.
