Industry 4.0 is leveraging the production capabilities of the industry. The deep digitalization that Industry 4.0 promotes enables to extend control skills to an exhaustive detail in the shop floors. Then, new planning strategies can be designed and implemented. We present mathematical models to represent non-permutation flow shop processes, incorporating Industry 4.0 features and customer-focused attention. Basically, we study the impact of lot streaming on the ensuing optimization problems, since the work-in-process inventory control is considerably enhanced by Industry 4.0 technologies. Thus, is possible to take advantage of subdividing the production lots into smaller sublots, as lot streaming proposes. To test this hypothesis we use a novel approach to non-permutation flow shop problems which requires a lot streaming strategy, incorporating total tardiness as objective function. Our analysis indicates that lot streaming improves results increasingly with the number of machines. We also find that the improvement is less steep with more sublots, increasing the computational cost of solutions. This indicates that it is highly relevant to fine tune the maximum number of sublots to avoid extra costs.