Sustainability decision making is a complex task for policy makers, considering the possible unseen consequences it may entail. With a broader scope covering environmental, economic, and social aspects, Life Cycle Sustainability Assessment (LCSA) is a promising holistic method to deal with that complexity. However, to date, this method is limited to the hotspot analysis of a product, service, or system, and hence only assesses direct impacts and overlooks the indirect ones (or consequences). This critical literature review aims to explore the challenges and the research gaps related to the integration of three methods in LCSA representing three pillars of sustainability: (Environmental) Life Cycle Assessment (LCA), Life Cycle Costing (LCC), and Social Life Cycle Assessment (S-LCA). The challenges and the research gaps that appear when pairing two of these tools with each other are identified and discussed, i.e., the temporal issues, different perspectives, the indirect consequences, etc. Although this study does not aim to remove the shadows in LCSA methods, critical research gaps are identified in order to be addressed in future works. More case studies are also recommended for a deeper understanding of methodological trade-offs that might happen, especially when dealing with the consequential perspective.