Multiple sclerosis (MS) lesion segmentation is crucial for monitoring disease progression. Deep learning methods have shown promising results but suffer from domain shift problems when evaluated in data from different protocols or scanners. Transfer learning (TL) achieves successful domain adaptation, but can lead to catastrophic forgetting, resulting in a significant performance drop on the source domain. Continuous learning aims to address this issue by retaining knowledge from previous domains while adapting to new ones. This work applies Elastic Weight Consolidation (EWC) for the first time in the context of domain-incremental learning for MS lesion segmentation. The approach was evaluated using a 3D U-Net trained on public datasets (WMH2017 and Shifts) and fine-tuned on an in-house dataset using both TL and EWC, in both full training and few-shot scenarios. Results show that with only 3 training images from the target domain, EWC leads to a 10% improvement in F-score, while using 5 images achieves similar results to using all available training images. Catastrophic forgetting was reduced by 8%-19% compared to standard TL, where performance drops ranged from 20 to 37%. This work demonstrates that EWC enables models to adapt to new domains while preserving previous knowledge, with minimal data requirements, advancing towards more generalizable deep learning models for clinical MS applications.