In real world, training data for person re-identification (Re-ID) is collected discretely with spatial and temporal variations, which requires a model to incrementally learn new knowledge without forgetting old knowledge. This problem is called lifelong person re-identification (LReID). Variations of illumination and background for images of each task exhibit task-specific image style and lead to task-wise domain gap. In addition to missing data from the old tasks, task-wise domain gap is a key factor for catastrophic forgetting in LReID, which is ignored in existing approaches for LReID. The model tends to learn task-specific knowledge with task-wise domain gap, which results in stability and plasticity dilemma. To overcome this problem, we cast LReID as a domain adaptation problem and propose a pseudo task knowledge preservation framework to alleviate the domain gap. Our framework is based on a pseudo task transformation module which maps the features of the new task into the feature space of the old tasks to complement the limited saved exemplars of the old tasks. With extra transformed features in the task-specific feature space, we propose a task-specific domain consistency loss to implicitly alleviate the task-wise domain gap for learning task-shared knowledge instead of task-specific one. Furthermore, to guide knowledge preservation with the feature distributions of the old tasks, we propose to preserve knowledge on extra pseudo tasks which jointly distills knowledge and discriminates identity, in order to achieve a better trade-off between stability and plasticity for lifelong learning with task-wise domain gap. Extensive experiments demonstrate the superiority of our method as compared with the state-of-the-art lifelong learning and LReID methods.