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In this paper, we show that the process of continually learning new tasks and memorizing previous tasks introduces unknown privacy risks and challenges to bound the privacy loss. Based upon this, we introduce a formal definition of Lifelong DP, in which the participation of any data tuples in the training set of any tasks is protected, under a consistently bounded DP protection, given a growing stream of tasks. A consistently bounded DP means having only one fixed value of the DP privacy budget, regardless of the number of tasks. To preserve Lifelong DP, we propose a scalable and heterogeneous algorithm, called L2DP-ML with a streaming batch training, to efficiently train and continue releasing new versions of an L2M model, given the heterogeneity in terms of data sizes and the training order of tasks, without affecting DP protection of the private training set. An end-to-end theoretical analysis and thorough evaluations show that our mechanism is significantly better than baseline approaches in preserving Lifelong DP. The implementation of L2DP-ML is available at: https://github.com/haiphanNJIT/PrivateDeepLearning.