[en] In this note we analyse the Lie algebras of physical states stemming from lattice constructions on general even, self-dual lattices Γ^p,q with p ≥ q. It is known that if the lattice is at most lorentzian, the resulting Lie algebra is of generalized Kac-Moody type (or has a quotient that is). We show that this is not true as soon as q ≥ 1. By studying a certain sublattice in the case q > 1 we obtain results that lead to the conclusion that the resulting non-GKM Lie algebra cannot be described conveniently in terms of generators and relations and belongs to a new and qualitatively different class of Lie algebras. (author)