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Adapting language models to learn continuously from data streams while retaining previous knowledge is a key challenge in artificial intelligence (AI), particularly in lifelong language learning. Existing distillation methods are based on offline techniques, limiting their ability to update in real-time and adapt to dynamic environments. To address this, we propose online dynamic mutual distillation - a novel framework that enables continuous mutual learning from task streams without relying on domain-specific teachers. To our knowledge, this is the first application of mutual learning in lifelong language learning, providing dynamic knowledge transfer without domain-specific teachers. Moreover, our extensive experiments demonstrate that the proposed method reduces catastrophic forgetting, while improving task performance on various benchmark datasets making it suitable for real-world, dynamic natural language processing (NLP) applications such as adaptive chatbots and personalized language systems. We will make our code publicly available upon acceptance.