Unsupervised domain adaptive person re-identification (ReID) has been extensively investigated to mitigate the adverse effects of domain gaps. Those works assume the target domain data can be accessible all at once. However, for the real-world streaming data, this hinders the timely adaptation to changing data statistics and sufficient exploitation of increasing samples. In this paper, to address more practical scenarios, we propose a new task, Lifelong Unsupervised Domain Adaptive (LUDA) person ReID. This is challenging because it requires the model to continuously adapt to unlabeled data of the target environments while alleviating catastrophic forgetting for such a fine-grained person retrieval task. We design an effective scheme for this task, dubbed CLUDA-ReID, where the anti-forgetting is harmoniously coordinated with the adaptation. Specifically, a meta-based Coordinated Data Replay strategy is proposed to replay old data and update the network with a coordinated optimization direction for both adaptation and memorization. Moreover, we propose Relational Consistency Learning for old knowledge distillation/inheritance in line with the objective of retrieval-based tasks. We set up two evaluation settings to simulate the practical application scenarios. Extensive experiments demonstrate the effectiveness of our CLUDA-ReID for both scenarios with stationary target streams and scenarios with dynamic target streams.