Accurate brain lesion segmentation in MRI is vital for effective clinical diagnosis and treatment planning. Due to high annotation costs and strict data privacy regulations, universal models require employing Continual Learning (CL) to adapt to evolving clinical tasks without losing previously acquired knowledge. However, existing CL paradigms often suffer from capacity limits or redundant parameter growth, and even advanced dynamic methods rely mostly on image-perception strategies that struggle to handle the substantial pathological and multimodal heterogeneity inherent in brain imaging. To address this issue, we propose Concept-Reasoning Expansion (CoRE) framework, which establishes a joint decision-making mechanism by integrating visual features with structured concepts. Through the alignment of image tokens with a hierarchical concept library, CoRE simulates clinical reasoning to guide both interpretable expert routing and demand-based model growth. This collaborative process ensures model evolution is grounded in clinical priors, preventing redundant parameter expansion while maximizing knowledge reuse. Extensive evaluations across 12 sequential brain lesion MRI tasks demonstrate that CoRE achieves state-of-the-art performance and provides a high knowledge starting point for efficient future adaptation. Its superior few-shot transferability and clinical interpretability further validate its effectiveness in managing non-stationary clinical data streams. Our code will be released soon.