Mobile sensing-based modeling of behavioral changes could predict an oncoming psychotic relapse in schizophrenia patients for timely interventions. Deep learning models could complement existing non-deep learning models for relapse prediction by modeling latent behavioral features relevant to the prediction. However, given the inter-individual behavioral differences, model personalization might be required for a predictive model. In this work, we propose RelapsePredNet, a Long Short-Term Memory (LSTM) neural network-based model for relapse prediction. The model is personalized for a particular patient by training using data from patients most similar to the given patient. Several demographics and baseline mental health scores were considered as personalization metrics to define patient similarity. We investigated the effect of personalization on training dataset characteristics, learned embeddings, and relapse prediction performance. We compared RelapsePredNet with a deep learning-based anomaly detection model for relapse prediction. Further, we investigated if RelapsePredNet could complement ClusterRFModel (a random forest model leveraging clustering and template features proposed in prior work) in a fusion model, by identifying latent behavioral features relevant for relapse prediction. The CrossCheck dataset consisting of continuous mobile sensing data obtained from 63 schizophrenia patients, each monitored for up to a year, was used for our evaluations. The proposed RelapsePredNet outperformed the deep learning-based anomaly detection model for relapse prediction. The F2 score for prediction were 0.21 and 0.52 in the full test set and the Relapse Test Set (consisting of data from patients who have had relapse only), respectively. These corresponded to a 29.4% and 38.8% improvement compared to the existing deep learning-based model for relapse prediction.