Recently, machine learning (ML) has become a popular approach to support self-adaptation. ML has been used to deal with several problems in self-adaptation, such as maintaining an up-to-date runtime model under uncertainty and scalable decision-making. Yet, exploiting ML comes with inherent challenges. In this paper, we focus on a particularly important challenge for learning-based self-adaptive systems: drift in adaptation spaces. With adaptation space we refer to the set of adaptation options a self-adaptive system can select from at a given time to adapt based on the estimated quality properties of the adaptation options. Drift of adaptation spaces originates from uncertainties, affecting the quality properties of the adaptation options. Such drift may imply that eventually no adaptation option can satisfy the initial set of the adaptation goals, deteriorating the quality of the system, or adaptation options may emerge that allow enhancing the adaptation goals. In ML, such shift corresponds to novel class appearance, a type of concept drift in target data that common ML techniques have problems dealing with. To tackle this problem, we present a novel approach to self-adaptation that enhances learning-based self-adaptive systems with a lifelong ML layer. We refer to this approach as lifelong self-adaptation. The lifelong ML layer tracks the system and its environment, associates this knowledge with the current tasks, identifies new tasks based on differences, and updates the learning models of the self-adaptive system accordingly. A human stakeholder may be involved to support the learning process and adjust the learning and goal models. We present a general architecture for lifelong self-adaptation and apply it to the case of drift of adaptation spaces that affects the decision-making in self-adaptation. We validate the approach for a series of scenarios using the DeltaIoT exemplar.