Critical hydrometeorological events are generally triggered by heavy precipitation. In complex terrain, precipitation may be perturbed by the upslope raising of the incoming humid airflow, causing in some cases extreme rainfall. In this work, the application of LUME—Linear Upslope Model Extension—to a group of extreme events that occurred across mountainous areas of the Central Alps and Apennines in Italy is presented. Based on the previous version, the model has been “extended” in some aspects, proposing a methodology for physically estimating the time-delay coefficients as a function of precipitation efficiency. The outcomes of LUME are encouraging for the cases studied, revealing the intensification of precipitation due to the orographic effect. A comparison between the reference rain gauge data and the results of the simulations showed good agreement. Since extreme precipitation is expected to increase due to climate change, especially across the Mediterranean region, LUME represents an effective tool to investigate more closely how these extreme phenomena originate and evolve in mountainous areas that are subject to potential hydrometeorological risks.