We investigate conduction and free-carrier injection in laterally doped GaAs p-i-n diodes formed in one and two-dimensional photonic crystal (PC) nanocavities. Finite element simulations show that the lateral geometry exhibits high conductivity for a wide range of PC parameters and allows for precise control over current flow, enabling efficient carrier injection despite fast surface recombination. Thermal simulations indicate that the temperature increase during steady-state operation is only 3.3 K in nanobeams and 0.29 K in L3 defect nanocavities. The results affirm the suitability of lateral doping in PC devices and indicate criteria for further design optimization.