The focus of our chapter is to determine the extent to which lean manufacturing and lean digital 4.0 are complementary when it comes to reducing waste in the production chain. Indeed, Industry 4.0 is increasingly presented as a must for improving productivity and ensuring economic growth in manufacturing companies. On the other hand, many companies have already partially or fully implemented Lean principles and tools. A number of aspects remain to be clarified regarding the existing links between Industry 4.0 and the Lean approach: is there a hierarchy, improvement or complementarity between the two approaches? What are the links between the two approaches? This chapter seeks to highlight the links that exist between the two approaches in terms of continuous improvement and operational performance. To this end, we have highlighted the principles and technologies proposed by lean manufacturing and Industry 4.0 respectively. We have also discussed the theory of constraints, which has been applied in lean manufacturing circles.