Vertically stacked 2D materials have provided an unprecedented platform to identify various physical properties and discover novel interfacial emergent phenomena. In this study, the lattice thermal conductivity of Janus WSSe bilayer, involving diverse interfacial stacking configurations, has been clarified by solving the phonon Boltzmann transport equation based on first-principles calculations. The effect of homogeneously stacking on thermal conductivity and potential modulation approaches has also been revealed for Janus WSSe. Our results indicate that the thermal transport in Janus WSSe bilayer can be suppressed by van der Waals interface, and depends on both the stacking patterns and interfacial compositions (S-S, Se-Se and Se-S interfaces). Moreover, the interface effect can be further modulated by an applied vertical pressure. A further reduction in thermal conductivity can be achieved for Janus WSSe bilayer under vertical pressure, implying great potential for efficient thermal management and sensing applications.