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The rapid evolution of legal concepts over time necessitates that legal language models adapt swiftly accounting for the temporal dynamics. However, prior works have largely neglected this crucial dimension, treating legal adaptation as a static problem rather than a continuous process. To address this gap, we pioneer LexTempus, a dynamic mixture of experts model that explicitly models the temporal evolution of legal language in a parameter-efficient online learning framework. LexTempus starts with a single lightweight adapter expert and dynamically expands by adding new experts as significant deviations in the data distribution are detected. This self-expansion strategy allows LexTempus to adapt to new information without forgetting past knowledge, thereby improving temporal generalization. We use a a non-parametric similarity-based router to merge relevant experts into a unified expert for each test instance, ensuring efficient inference without additional overhead. We validate the effectiveness of LexTempus on ECHR and EU case law datasets, demonstrating its superiority in both perplexity and open-ended text generation quality metrics.