Collaborative filtering drives many successful recommender systems but struggles with fine-grained user-item interactions and explainability. As users increasingly seek transparent recommendations, generating textual explanations through language models has become a critical research area. Existing methods employ either RNNs or Transformers. However, RNN-based approaches fail to leverage the capabilities of pre-trained Transformer models, whereas Transformer-based methods often suffer from suboptimal adaptation and neglect aspect modeling, which is crucial for personalized explanations. We propose ELIXIR (Efficient and LIghtweight model for eXplaIning Recommendations), a multi-task model combining rating prediction with personalized review generation. ELIXIR jointly learns global and aspect-specific representations of users and items, optimizing overall rating, aspect-level ratings, and review generation, with personalized attention to emphasize aspect importance. Based on a T5-small (60M) model, we demonstrate the effectiveness of our aspect-based architecture in guiding text generation in a personalized context, where state-of-the-art approaches exploit much larger models but fail to match user preferences as well. Experimental results on TripAdvisor and RateBeer demonstrate that ELIXIR significantly outperforms strong baseline models, especially in review generation.