  We provide a new class of Z_N x Z_M heterotic orbifolds on non-factorisable
tori, whose boundary conditions are defined by Lie lattices. Generally, point
groups of these orbifolds are generated by Weyl reflections and outer
automorphisms of the lattices. We classify abelian orbifolds with and without
discrete torsion. Then we find that some of these models have smaller Euler
numbers than those of models on factorisable tori T^2 x T^2 x T^2. There is a
possibility that these orbifolds provide smaller generation numbers of N=1
chiral matter fields than factorisable models.
