The occurrence of flash floods in urban catchments within the Mediterranean climate zone has witnessed a substantial rise due to climate change, underscoring the urgent need for early-warning systems. This paper examines the implementation of an early flood monitoring and forecasting system (EMFS) to predict the critical overflow level of a small urban stream on Lesvos Island, Greece, which has a history of severe flash flood incidents requiring rapid response. The system is supported by a network of telemetric stations that measure meteorological and hydrometric parameters in real time, with a time step accuracy of 15 min. The collected data are fed into the physical Hydrologic Engineering Center’s Hydrologic Modeling System (HEC-HMS), which simulates the stream’s discharge. Considering the HEC-HMS’s estimated outflow and other hydro-meteorological parameters, the EMFS uses long short-term memory (LSTM) neural networks to enhance the accuracy of flood prediction. In particular, LSTMs are employed to analyze the real-time data from the telemetric stations and make multi-step predictions of the critical water level. Hydrological time series data are utilized to train and validate the LSTM models for short-term leading times of 15 min, 30 min, 45 min, and 1 h. By combining the predictions obtained by the HEC-HMS with those of the LSTMs, the EMFS can produce accurate flood forecasts. The results indicate that the proposed methodology yields trustworthy behavior in enhancing the overall resilience of the area against flash floods.