Anomaly detection is of paramount importance in many real-world domains, characterized by evolving behavior. Lifelong learning represents an emerging trend, answering the need for machine learning models that continuously adapt to new challenges in dynamic environments while retaining past knowledge. However, limited efforts are dedicated to building foundations for lifelong anomaly detection, which provides intrinsically different challenges compared to the more widely explored classification setting. In this paper, we face this issue by exploring, motivating, and discussing lifelong anomaly detection, trying to build foundations for its wider adoption. First, we explain why lifelong anomaly detection is relevant, defining challenges and opportunities to design anomaly detection methods that deal with lifelong learning complexities. Second, we characterize learning settings and a scenario generation procedure that enables researchers to experiment with lifelong anomaly detection using existing datasets. Third, we perform experiments with popular anomaly detection methods on proposed lifelong scenarios, emphasizing the gap in performance that could be gained with the adoption of lifelong learning. Overall, we conclude that the adoption of lifelong anomaly detection is important to design more robust models that provide a comprehensive view of the environment, as well as simultaneous adaptation and knowledge retention.