Many industrial sectors seek to improve their management by applying new methods, often implementing innovative procedures since they are forced to adapt to 4.0 technology, of which financial institutions are not far from this reality. This article develops the union of two well-known methodologies, but together, that is, the Lean Management methodology and the Cloud Computing methodology. The union of these two methodologies, Lean Computing is born, which will help to know what its impact is with industry 4.0 to improve the management of internal attentions in terms of a financial institution. The methodology used for the development of this topic is of the applied type, it has a pre-experimental quantitative approach based on a study group, both pretest and posttest. Likewise, it has an application link since it requires a positive transformation of the problem. After the application of this methodology, it was obtained that productivity increased by 52%, the cost gained by 68%, while the invested cost decreased by 38% and the lost cost by 55%, all of these while the invested cost decreased by 38% and the lost cost by 55%, all of these comparing the results of the pretest and posttest taken in a period of time of 30 days. Whit theses results it can be seen that the implementation of this new methodology has positive impacts and is of great help to the entity under study.