Lean management has been implemented successfully to improve efficiency in supply chain processes. With the progression and implementation of Industry 4.0, there is an increase in digitization actions to focus on greater business results and productivity. Major organizations are focusing on implementing Industry 4.0 initiatives in supply chain processes to advance efficiency and productivity. It is uncertain whether the implementation of industry 4.0 applications is in line with existing continuous improvement techniques such as lean management, which is known to have benefits in advancing business objectives. Therefore, this research is important in further exploring the synergies and practical implementation of both Industry 4.0 & lean management. This review looks at the practical applications of lean management and eleven industry 4.0 digitization enablers. The critical review of selected journal articles highlighting practical applications of the concept and integrative models was done to look at the integration models within industry 4.0 (horizontal, vertical & end-to-end engineering integrations) and challenges in adoption of the integration models. It further reviews the model of integration of lean management and the three industry 4.0 integrations and how they can be combined together in a practical manner for organizational benefits.