The Lorenz ratios (L = κ/σT) of the Dirac-fermion systems were numerically calculated using the Boltzmann transport theory, where κ, σ and T are the thermal conductivity, electrical conductivity and absolute temperature, respectively. The bipolar-diffusion effect, which enhances the electronic thermal conductivity κ_e in intrinsic semiconductors, was introduced to account for the reported giant L of a Dirac-fermion system, graphene at its neutrality condition. It was found that the calculations qualitatively reproduce the experimentally observed gate-voltage dependence of σ , S and κ_e by considering the energy dependence of the relaxation time; and the electron- and hole-puddles. The calculated value of L amounts to (2?4)L₀, where L₀= 2.45 × 10^-8 W・Ω・K^-2 is Sommerfeld value of Wiedemann-Franz law, while the reported ?? of graphene reaches about 20L₀ at most. The rather large L (=3.7L₀) was also observed for another Dirac-fermion system, α-(BEDT-TTF)₂I₃ (BEDT-TTF = bis(ethylenedithio)tetrathiafulvalene) by measuring simultaneously the change in the σ and κ associated with its charge-ordering transition at about 135 K for a single crystal. Another explanation of the giant L on the basis of quantum hydrodynamics is also introduced briefly, while both the bipolar-diffusion and quantum-hydrodynamic mechanisms are not exclusive to each other.