Thermal conductivities (k,keff) have been estimated for sintered and sphere-pac Li2O and γ-LiAlO2 with and without neutron irradiation effects. The estimation is based on (a) data from unirradiated UO2, Li2O, and γ-LiAlO2; (b) data from irradiated dielectric insulator materials; and (c) relatively simple physical models. Comparison of model predictions with limited ex- and in-reactor data found reasonable agreement, thus lending credence for their use in design applications. The impact of thermal conductivities on tritium breeding and power generation infusion solid breeder blankets is briefly highlighted.