Lean Six Sigma (LSS) is an approach that is widely recognised as useful for improving operational performance. Despite this recognition, it is difficult to implement and failures are common. It is necessary to understand the key factors that are critical to the successful LSS implementation. These factors are often referred to as Critical Success Factors (CSFs).  Despite being a consolidated research area, recent reviews lack comprehensive exploration of LSS CSFs. This paper aims to present a comprehensive and critical review of this research area evolution, identifying the main CSFs and the relationships between them, the topics being researched in this field, and research gaps. A Systematic Literature Review (SLR) was used to develop this article. The results show that the published documents have been increasing in the domain, but impact have been decreasing. The review identified the ten most relevant CSFs. The most relevant factors is management commitment, which drive others. The CSFs were identified in micro, small and medium enterprises (MSMEs), in service organisations, used for assessment tools, LSS leadership, and used as an integrated approach in Industry 4.0. The latter is an emerging issue that requires more research. This article presents evidence that LSS CSFs are acknowledged and vary little from organisation to organisation. Additional empirical research is needed to validate whether the identified CSFs are the most relevant in real settings.