The aim of this article is to improve the performance of production systems by integrating Lean tools and functionalities from the design phase, thereby reducing the need to apply them during the use phase of future manufacturing systems. This implies a change of mindset; instead of reacting to problems as they arise and then implementing Lean to remedy them, companies should proactively integrate it from the design phase. However, trying to integrate several Lean tools and functionalities into the design of a production system to satisfy multiple performance criteria can generate contradictions. For this reason, we propose a new methodology: Lean Parameter Integration Matrix (LPIM), which can be used to resolve the different types of problems. LPIM contains a set of generalized Lean parameters extracted from the Lean tools most used in companies. It allows the simultaneous identification of technical and physical contradictions that may arise from the integration of multiple Lean tools and their functionalities, and provides guidance for their resolution, using the principles of TRIZ methodology for resolving technical and physical contradictions.