Longitudinal experiential data offers rich insights into dynamic human states, yet building models that generalize across diverse contexts remains challenging. This paper addresses how to best represent multi-modal longitudinal experiential data as text and formulate prediction tasks to maximize large language model (LLM) cross-distribution generalization. We propose ConText-LE, a framework grounded in linguistic and cognitive theories of contextual meaning-making, which systematically investigates text representation strategies and output formulations for robust behavioral forecasting. Our novel Meta-Narrative representation synthesizes complex temporal patterns into semantically rich narratives, while Prospective Narrative Generation reframes prediction as a generative task aligned with LLMs' inherent contextual understanding capabilities. Through comprehensive experiments on three diverse longitudinal datasets, we address the critical but underexplored challenge of cross-distribution generalization in mental health and educational behavior forecasting. We demonstrate that combining Meta-Narrative input with Prospective Narrative Generation significantly outperforms existing LLM-based approaches, achieving up to 12.28% improvement in out-of-distribution accuracy and up to 11.99% improvement in F1 scores over binary classification methods. Bidirectional evaluation and architectural ablation studies confirm the robustness of our approach, establishing ConText-LE as an effective framework for developing reliable behavioral forecasting systems across temporal and contextual shifts.