Semiconductors are ubiquitous gain media for coherent light sources. Solution-processed three-dimensional (3D) halide perovskites (e.g., CH3NH3PbI3) with their outstanding room temperature optical gain properties are the latest members of this family. Their two-dimensional (2D) layered perovskite counterparts with natural multiple quantum well structures exhibit strong light-matter interactions and intense excitonic luminescence. However, despite such promising traits, there have been no reports on room temperature optical gain in 2D layered perovskites. Herein, we reveal the challenges towards achieving amplified spontaneous emission (ASE) in the archetypal (C6H5C2H4NH3)2PbI4 (or PEPI) system. Temperature-dependent transient spectroscopy uncovers the dominant free exciton trapping and bound biexciton formation pathways that compete effectively with biexcitonic gain. Phenomenological rate equation modeling predicts a large biexciton ASE threshold of ∼1.4 mJ cm(-2), which is beyond the damage threshold of these materials. Importantly, these findings would rationalize the difficulties in achieving optical gain in 2D perovskites and provide new insights and suggestions for overcoming these challenges.