Type 1 Diabetes mellitus (T1D) is a widespread disease characterized by a persistent condition of hyperglycemia. Continuous Glucose Monitoring (CGM) devices allow people with T1D to keep track of their glycemic level for 24 hours a day. Artificial intelligence models can aid people with T1D adjusting and optimizing their insulin therapy by providing a prediction of the future glycemic level based on CGM data; nonetheless, most of them are large models that run on the cloud, whereas few studies have focused on the application on an edge device. Applying a data-driven model that must be continuously updated on an edge-computing system requires a compromise between the predictive model performance and the limited computational capability of the edge device. In this study, we investigate different training approaches of a well-established Long Short-Term Memory neural network for blood glucose level forecasting in people with T1D based on CGM and insulin data. The best performance is achieved when the model is pre-trained on a large amount of data from 10 virtual patients, and fine-tuned on patient-specific data updating only the parameters of the output layer, while keeping the parameters of the hidden layers unchanged. The numeric results are comparable to those achieved by larger models in the literature. The presented model is characterized by an average training and DRQ time of 67.6 seconds on an edge device that is largely acceptable in practical cases.