  We consider spatially homogeneous Lifshitz black hole solutions in five
dimensional higher derivative gravity theories, which can be possible near
horizon geometries of some systems that are interesting in the framework of
gauge/gravity duality. We show the solutions belonging to the nine Bianchi
classes in the pure R^2 gravity. We find that these black holes have zero
entropy at non-zero temperatures and this property is the same as the case of
BTZ black holes in new massive gravity at the critical point. In the most
general quadratic curvature gravity theories, we find new solutions in Bianchi
Type I and Type IX cases.
