  Let $\Lambda$ be a lattice of rank $n$. A Lie algebra on the lattice
$\Lambda$ is a Lie algebra ${\cal L}=\oplus_{\lambda\in\Lambda}\,{\cal
L}_{\lambda}$ such that $\dim\,{\cal L}_\lambda=1$ for all $\lambda$. In this
article, we classify all simple graded Lie algebras on a lattice.
