The intrinsic B-site antisite defects fundamentally constrain the performance of double halide perovskites Cs2AgBiCl6 and Cs2AgInCl6. The resulting partially disordered or fully disordered structures exhibit distinct optoelectronic properties. Herein, we performed first-principles calculations to explore the accessibility of B-site cation disordering in Cs2AgBiCl6 and Cs2AgInCl6 and its effects on the electronic structures of both these double perovskites. It was revealed that the formation of cation-disordered Cs2AgBiCl6 required a lower energy cost than cation-disordered Cs2AgInCl6. Generally, the lone-pair electrons of Bi3+ make its electron configuration distinct from Ag+, which results in much higher energy cost for electronic relaxation during cation disordering of Cs2AgBiCl6. However, the more significant lattice relaxation of Cs2AgBiCl6 effectively reduced the energy cost of cation disordering. Furthermore, the resulting remarkable ionic relaxation and change in electronic redistribution in the cation-disordered Cs2AgBiCl6 effectively protected its electronic structure from the influence of cation disordering. Alternatively, cation disordering significantly influenced the electronic structure of Cs2AgInCl6. Our results provide an in-depth understanding on the lone-pair effect on cation disordering and electronic properties of double halide perovskites, which may be useful in the development and design of high-performance optoelectronic and photovoltaic devices based on double perovskites.