The purpose of this research work is to provide supply chain managers with a formal and generalizable approach that furnishes accurate guidelines to achieve a 2D performance integrating both Lean and Green. Despite the fact that several research works have been conducted in the framework of Lean and Green, at a conceptual level, the relationship between both paradigms is still ambiguous. Furthermore, the literature revealed a lack of relevant and generalizable approaches that explicitly demonstrate how to successfully implement Lean and Green in a relevant and integrated way. Since risks are the main obstacles disrupting performance, this research work addresses the identified gap by proposing a risk management approach (RMA) for Lean Green performance in a supply-chain context. Risk cannot be managed if not well-identified; hence, a rigorous literature investigation was conducted to define this concept in a supply-chain context. Later, risk was introduced into Lean and Green aspects. Subsequently, through a comprehensive review of previous risk identification studies, a novel classification of supply chain risks in a Lean Green context was provided. At a corporate level, risks often include several sources that cannot be treated at once. Therefore, a risk assessment analysis was performed, employing an analytic hierarchy process for its ease of use and broad adaptability. The output of this analysis provides visibility for an organization’s position toward performance goals and underlines crucial risks to be addressed. The risk treatment process was upgraded in this approach to a detailed analysis that aims at investigating the root causes behind the prioritized risks. Deployment of the approach on a corporate level revealed that treating a risk may negatively affect treating another. Indeed, thinking Lean is not necessarily Green, which stands with the fact that Lean Green supply chain challenges may outstrip classic optimization methods and techniques; therefore, its management requires innovative approaches. Thereby, our findings support the applicability and efficiency of the Theory of Inventive Problem Solving (TRIZ) in this setting. Although the case study focused on a specific company, the developed framework can be customized to fit different cases.