Lean Management and Six Sigma are nowadays applied not only to the manufacturing industry but also to service industry and public administration. The manifold variables affecting the Health Care system minimize the effect of a narrow Lean intervention. Therefore, this paper aims to discuss a comprehensive, system-based approach to achieve a factual holistic optimization of patient flows. This paper debates the efficacy of Lean principles applied to the optimization of patient flows and related activities, structures, and resources, developing a theoretical framework based on the principles of the Axiomatic Design. The demand for patient-oriented and efficient health services leads to use these methodologies to improve hospital processes. In the framework, patients with similar characteristics are clustered in families to achieve homogeneous flows through the value stream. An optimization checklist is outlined as the result of the mapping between Functional Requirements and Design Parameters, with the right sequence of the steps to optimize the patient flow according to the principles of Axiomatic Design. The Axiomatic Design-based top-down implementation of Health Care evidence, according to Lean principles, results in a holistic optimization of hospital patient flows, by reducing the complexity of the system.