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The enterprises to be competitive are constantly looking for continuous increase of productivity, quality and level of services. With the development of Industry 4.0 concept, manufacturers are more confident about new advantages of automation and systems integration. Lean management is well developed and empirically proven effective managerial approach. Combining Lean and Industry 4.0 practices seems to be necessary evolutionary step for further raise the level of operational excellence (exploitation of finance, workload, materials, machines/ devices). There is an increasing number of Industry 4.0 solutions used to reduce waste (as known from Lean Management). Therefore, the main objective of this article aims at presenting the results of a literature review on the concept of ‘Lean Industry 4.0ʹ. Dynamic methodology called “Systematic Literature Network Analysis (SLNA)” was used. It combines the Systematic Literature Review approach with the quantitative analysis of bibliographic networks to detect emerging topics and the dynamic evolution of the topics. The paper is a comprehensive systematization and rationalization of knowledge about the integration of LM and I4.0 concepts, identifies the most important research trends and defines directions for future research. The article contains a framework that presents the current state of knowledge in the area of Lean Industry 4.0., This research was funded by The Polish National Agency for Academic Exchange under grant no. PPI/APM/2018/1/ 00047 entitled ‘Industry 4.0 in Production and Aeronautical Engineering’ (International Academic Partnerships Programme).This work was supported by the The Polish National Agency for Academic Exchange [PPI/APM/2018/1/00047] and Industry 4.0 in Production and Aeronautical Engineering (International Academic Partnerships Program).