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Open Source Software (OSS) projects follow diverse lifecycle trajectories shaped by evolving patterns of contribution, coordination, and community engagement. Understanding these trajectories is essential for stakeholders seeking to assess project organization and health at scale. However, prior work has largely relied on static or aggregated metrics, such as project age or cumulative activity, providing limited insight into how OSS sustainability unfolds over time. In this paper, we propose a hierarchical predictive framework that models OSS projects as belonging to distinct lifecycle stages grounded in established socio-technical categorizations of OSS development. Rather than treating sustainability solely as project longevity, these lifecycle stages operationalize sustainability as a multidimensional construct integrating contribution activity, community participation, and maintenance dynamics. The framework combines engineered tabular indicators with 24-month temporal activity sequences and employs a multi-stage classification pipeline to distinguish lifecycle stages associated with different coordination and participation regimes. To support transparency, we incorporate explainable AI techniques to examine the relative contribution of feature categories to model predictions. Evaluated on a large corpus of OSS repositories, the proposed approach achieves over 94\% overall accuracy in lifecycle stage classification. Attribution analyses consistently identify contribution activity and community-related features as dominant signals, highlighting the central role of collective participation dynamics.