  Four-dimensional, oriented Lie algebras $\mathfrak{g}$ which satisfy the
tame-compatible question of Donaldson for all almost complex structures $J$ on
$\mathfrak{g}$ are completely described. As a consequence, examples are given
of (non-unimodular) four-dimensional Lie algebras with almost complex
structures which are tamed but not compatible with symplectic forms.
