Outlet boundary conditions (OBCs) and their numerical descriptions are critical to computational fluid dynamics (CFD) since they have significant influence on the numerical accuracy and stability. They present significant challenges to the two-phase lattice Boltzmann (LB) method, especially in the limit of large density ratio. In this study, three commonly used OBCs: convection boundary condition (CBC), Neumann boundary condition (NBC), and extrapolation boundary condition (EBC), are investigated and improved on basis of two LB models for large density ratios (single and double distribution function models). The existing numerical schemes for the OBCs are not directly applicable to the LB models because of the deviation of the momentum balance at the outlet boundary. The deviation becomes substantial at a large density ratio. Thus, in this work, modified OBC schemes are proposed to make the OBCs suitable for the two-phase LB models by adding an independent equation to obtain the outlet velocity. Numerical tests on droplet flowing in a channel are performed to evaluate the performance of the modified OBC schemes. Results indicate that the modified OBC schemes may be extended to tackle large density ratio situations. The modified NBC and EBC schemes are only suitable for the LB model with single distribution function. Three modified CBC schemes exhibit optimum performance for both single and double distribution function LB models which can be implemented for large density ratios.