  We study 4-dimensional second-Chern-Einstein almost-Hermitian manifolds. In
the compact case, we observe that under a certain hypothesis the Riemannian
dual of the Lee form is a Killing vector field. We use that observation to
describe 4-dimensional compact second-Chern-Einstein locally conformally
symplectic manifolds and we give some examples of such manifolds. Finally, we
study the second-Chern-Einstein problem on unimodular almost-abelian Lie
algebras, classifying those that admit a left-invariant second-Chern-Einstein
metric with a parallel non-zero Lee form.
