Many studies have been and are being published about the lean production system. The focus of those studies is placed on the elimination of wastes that result in the overall cost reduction. This paper sheds a new light on the analysis of the lean production system from the perspective of its goals classification. The categorization has the merit to reveal not only the nature of the different of goals but also to show their hierarchy and how the different hierarchical levels are related to each other. Furthermore, the clarification of the nature of lean production system goals suggests and implies that goals that seem out of reach, i.e. asymptotic goals, are the internal engine that can keep a company looking continuously for better ways to reduce production costs. In the traditional manufacturing, setting apparently unreachable goals goes against the conventional wisdom that considers them to contribute to the image of a poor performance especially by the external evaluations. This study demonstrates the importance and the necessity of asymptotic goals for the lean production system.