Lean-sustainability principles share two basic standards: waste minimization and enhanced value. The purpose of this research is to offer a conceptual model for assessing construction firms’ lean sustainability by evaluating the synergy between lean operations and sustainability using a multi-grade fuzzy method. Three enablers, fifteen criteria, and forty-four attributes were identified based on an exhaustive literature analysis and expert opinion. The multi-grade fuzzy approach is utilized in this study to measure the lean-sustainability in the case construction organization. The determined total lean-sustainability index of 7.5, which falls between the range of 6–8, demonstrates that the case construction organizations prioritize lean-sustainability. IPA technique is utilized to identify the weaker and stronger attributes of lean sustainability in the case organization that hinder the lean-sustainability overall performance. To identify the critical and triggering attributes, Graphic Theoretic (GT) Approach is utilized through sensitivity analysis. GT evaluates the weaker and stronger attributes in order to identify the essential and triggering attributes that will boost lean sustainability. Theoretically, this study contributes by providing a paradigm for assessing lean sustainability. This research can help construction organizations discover essential lean-sustainability practices on a regular basis and concentrate on their weaker attributes in order to advance their performance.