Application of the lattice Boltzmann method (LBM) has been extended to formulate and solve the energy equation of a non-Fourier conduction and radiation heat transfer problem in a concentric spherical shell. The enclosed conducting-radiating medium is absorbing, emitting and scattering. The non-Fourier conduction effect is induced by thermally perturbing one of the boundaries and incorporating the finite propagation speed of the thermal wave front in Fourier's law of heat conduction. The volumetric radiative information needed in the energy equation has been computed using the finite volume method (FVM). To establish the accuracy of the LBM approach, with volumetric radiative information obtained from the FVM, the energy equation is also solved using the FVM. Effects of extinction coefficient, scattering albedo, conduction-radiation parameter, emissivity, radius ratio and the magnitude of thermal perturbations are studied on transient temperature distributions. Effects of the aforesaid parameters on the steady-state conduction, radiation and total energy flow rates are also studied. Steady-state LBM and FVM results are compared. In all the cases, the LBM results compare exceedingly well with the FVM results, and LBM has a faster convergence than the FVM. (C) 2013 Elsevier Ltd. All rights reserved.