  In this note we analyse the Lie algebras of physical states stemming from
lattice constructions on general even, self-dual lattices Gamma^{p,q} with p
greater or equal to 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 is larger than 1. By
studying a certain sublattice in the case q>1 we obtain results that lead to
the conjecture 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.
