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We provide a new class of Z_N x Z_M heterotic orbifolds on non-factorisabletori, whose boundary conditions are defined by Lie lattices. Generally, pointgroups of these orbifolds are generated by Weyl reflections and outerautomorphisms of the lattices. We classify abelian orbifolds with and withoutdiscrete torsion. Then we find that some of these models have smaller Eulernumbers than those of models on factorisable tori T^2 x T^2 x T^2. There is apossibility that these orbifolds provide smaller generation numbers of N=1chiral matter fields than factorisable models.Comment: 24 pages, 5 figures; v2: a few errors on tables are corrected, typos  corrected, version to appear in JHE

Heterotic orbifold models on Lie lattice with discrete torsion