Lean and six sigma approaches contribute to the development of processes with less waste and variability. The sustainability of processes the introduction of routines aimed at environmental well-being. Lean production methods, along with a sustainable supply chain, ensure cooperation, trust, reduced waste and process variation. Evidence suggests that organizations find the integration between these themes challenging. Thus, the objective of the research is to analyze the academic literature on the practical application of lean six sigma in the context of the supply chain. The method used was the critical review of the literature, to build the research gap and subsequently build the proposed methodological framework. As a result, the article presents characteristics of the literature for the application of Green Lean Six Sigma in the supply chain and identifies the tools that are used in the case studies that made up the research database.