Rail irregularity presents a major threat to the high-speed train (HST) safety on a high-speed rail (HSR) bridge. Lateral bridge deformation has a significant impact on geometric parameters of the rail. In this paper, the influence of lateral bridge deformation on the train operation on the HSR bridge is investigated. Variational calculus is employed to establish the analytical mapping between the lateral bridge and rail deformation. By superimposing the mapped rail deformation and initial random rail irregularity, the composed rail unevenness under lateral bridge deformation is obtained. Thereafter, by adopting the dynamical model of the train-track-bridge coupling system (TTBCS), the dynamic behaviour of the train moving across the HSR track-bridge system is analysed. Based on safety and comfortability control indicators of the HST operation, effects of different types of lateral bridge deformations with various amplitudes on the train’s operation performances are investigated. The results indicate that the bilateral girder’s mutual translation has the most significant impact on the train’s operation. When the HST is moving with the velocity of 350 km/h, lateral bridge deformation amplitude thresholds are suggested as 17.43 and 8.12 mm to ensure the safety and comfortability of the HST operation, respectively. The obtained results can provide beneficial pointers for HSR bridge design.