  Let G be a Lie group equipped with a left-invariant semi-Riemannian metric.
Let K be a semisimple subgroup of G generating a left-invariant conformal
foliation F of codimension two on G. We then show that the foliation F is
minimal. This means that locally the leaves of F are fibres of a complex-valued
harmonic morphism. In the Riemannian case, we prove that if the metric
restricted to K is biinvariant then F is totally geodesic.
