  Let $(G,g)$ be a 4-dimensional Riemannian Lie group with a 2-dimensional
left-invariant, conformal foliation $\F$ with minimal leaves. Let $J$ be an
almost Hermitian structure on $G$ adapted to the foliation $\F$. We classify
such structures $J$ which are almost K\"ahler $(\A\K)$, integrable $(\I)$ or
K\"ahler $(\K)$. Hereby we construct several new multi-dimensional examples in
each class.
