Lean manufacturing has been used by companies for decades to achieve their objectives. In today's context the introduction of industry 4.0 technologies has become imminent. However, the way these two paradigms can be mixed up in a common approach is yet not mature. Previous attempts to combine Lean and industry 4.0 have been led in literature. In this paper, we show our positioning and a global methodology of modeling that we undertake. The study of the relationship is shown in this document based on case studies reviewed in the literature. Initial modeling of influence will help in the gradual building of the global methodology. An example of Kanban and digitalization is depicted. The target is to illustrate the possible ways of combination of these two performance paradigms who lead implementation of Lean and industry 4.0 technology transformation.