  Any pseudo-Hermitian or para-Hermitian manifold of dimension 4 admits a
unique Kaehler-Weyl structure; this structure is locally conformally Kaehler if
and only if the alternating Ricci tensor vanishes. The alternating Ricci tensor
takes values in a certain representation space. In this paper, we show that any
algebraic possibility in this representation space can in fact be geometrically
realized by a left-invariant Kaehler-Weyl structure on a 4-dimensional Lie
group in either the Hermitian or the para-Hermitian setting.
