  We consider Gauss-Bonnet (GB) gravity in general dimensions, which is
non-minimally coupled to a scalar field. By choosing the scalar potential of
the type $V(\phi)=2\Lambda_0+\fft 12m^2\phi^2+\gamma_4\phi^4$, we first obtain
large classes of scalar hairy black holes with spherical/hyperbolic/planar
topologies that are asymptotic to locally anti-de Sitter (AdS) space-times. We
derive the first law of black hole thermodynamics using Wald formalism. In
particular, for one class of the solutions, the scalar hair forms a
thermodynamic conjugate with the graviton and nontrivially contributes to the
thermodynamical first law. We observe that except for one class of the planar
black holes, all these solutions are constructed at the critical point of GB
gravity where there exists an unique AdS vacua. In fact, Lifshitz vacuum is
also allowed at the critical point. We then construct many new classes of
neutral and charged Lifshitz black hole solutions for a either minimally or
non-minimally coupled scalar and derive the thermodynamical first laws. We also
obtain new classes of exact dynamical AdS and Lifshitz solutions which describe
radiating white holes. The solutions eventually become an AdS or Lifshitz vacua
at late retarded times. However, for one class of the solutions the final state
is an AdS space-time with a globally naked singularity.
