Organic-inorganic lead halide quasi-two-dimensional (2D) perovskites are promising gain media for lasing applications because of their low cost, tunable colour, excellent stability and solution processability . Optically pumped continuous-wave (CW) lasing is highly desired for practical applications in high-density integrated optoelectronics devices and constitutes a key step towards electrically pumped lasers . However, CW lasing has not yet been realized at room temperature because of the 'lasing death' phenomenon (the abrupt termination of lasing under CW optical pumping), the cause of which remains unknown. Here we study lead halide-based quasi-2D perovskite films with different organic cations and observe that long-lived triplet excitons considerably impede population inversion during amplified spontaneous emission and optically pumped pulsed and CW lasing. Our results indicate that singlet-triplet exciton annihilation is a possible intrinsic mechanism causing lasing death. By using a distributed-feedback cavity with a high quality factor and applying triplet management strategies, we achieve stable green quasi-2D perovskite lasers under CW optical pumping in air at room temperature. We expect that our findings will pave the way to the realization of future current-injection perovskite lasers.