Multiple sclerosis lesions influence the process of image analysis, leading to tissue segmentation problems and biased morphometric estimates. Existing techniques try to reduce this bias by filling all lesions as normal-appearing white matter on T1-weighted images, considering each time-point separately. However, due to lesion segmentation errors and the presence of structures adjacent to the lesions, such as the ventricles and deep grey matter nuclei, filling all lesions with white matter-like intensities introduces errors and artefacts. In this paper, we present a novel lesion filling strategy inspired by in-painting techniques used in computer graphics applications for image completion. The proposed technique uses a five-dimensional (5D), patch-based (multi-modality and multi-time-point), Non-Local Means algorithm that fills lesions with the most plausible texture. We demonstrate that this strategy introduces less bias, fewer artefacts and spurious edges than the current, publicly available techniques. The proposed method is modality-agnostic and can be applied to multiple time-points simultaneously. In addition, it preserves anatomical structures and signal-to-noise characteristics even when the lesions are neighbouring grey matter or cerebrospinal fluid, and avoids excess of blurring or rasterisation due to the choice of the segmentation plane, shape of the lesions, and their size and/or location.