This study explores how the integration of cognitive robotic systems into lean manufacturing can simultaneously address the elimination of the seven classical wastes and support sustainable development in Ukrainian enterprises. A simulation-based methodology was applied, using a digital twin of a manufacturing system. Three scenarios were compared: (A) baseline operations with traditional lean practices, (B) conventional automation, and (C) integration of cognitive robotics. Key performance indicators (OEE, lead time, FPY, scrap rate, energy consumption, and inventory levels) were used for evaluation. The results show that cognitive robotics reduces order fulfillment time by more than 30%, lowers defect rates by over 70%, and decreases energy consumption per unit of production by about 20%. At the same time, first-pass yield (FPY) and overall equipment effectiveness (OEE) significantly increase. Cognitive robotic systems provide measurable advantages compared to both traditional lean and conventional automation, confirming their role as a driver of sustainable competitiveness. For manufacturing and Ukrainian manufacturing, cognitive robotics can mitigate labor shortages, improve supply chain resilience, and reduce costs while supporting sustainable development goals (SDGs). The Lean 5.0 framework may serve as a strategic basis for post-war industrial recovery and modernization.