Robots will experience non-stationary environment dynamics throughout their lifetime: the robot dynamics can change due to wear and tear, or its surroundings may change over time. Eventually, the robots should perform well in all of the environment variations it has encountered. At the same time, it should still be able to learn fast in a new environment. We identify two challenges in Reinforcement Learning (RL) under such a lifelong learning setting with off-policy data: first, existing off-policy algorithms struggle with the trade-off between being conservative to maintain good performance in the old environment and learning efficiently in the new environment, despite keeping all the data in the replay buffer. We propose the Offline Distillation Pipeline to break this trade-off by separating the training procedure into an online interaction phase and an offline distillation phase.Second, we find that training with the imbalanced off-policy data from multiple environments across the lifetime creates a significant performance drop. We identify that this performance drop is caused by the combination of the imbalanced quality and size among the datasets which exacerbate the extrapolation error of the Q-function. During the distillation phase, we apply a simple fix to the issue by keeping the policy closer to the behavior policy that generated the data. In the experiments, we demonstrate these two challenges and the proposed solutions with a simulated bipedal robot walk-ing task across various environment changes. We show that the Offline Distillation Pipeline achieves better performance across all the encountered environments without affecting data collection. We also provide a comprehensive empirical study to support our hypothesis on the data imbalance issue.