Multiple Sclerosis lesions influence the process of image analysis, leading to tissue segmentation problems and biased morphometric estimates. With the aim of reducing this bias, existing techniques fill segmented lesions as normal appearing white matter. However, due to lesion segmentation errors or the presence of neighbouring structures, such as the ventricles and deep grey matter structures, filling all lesions as white matter like intensities is prone to introduce errors and artefacts. In this paper, we present a novel lesion filling strategy based on in-painting techniques for image completion. This technique makes use of a patch-based Non-Local Means algorithm that fills the lesions with the most plausible texture, rather than normal appearing white matter. We demonstrate that this strategy introduces less bias and fewer artefacts and spurious edges than previous techniques. The advantages of the proposed methodology are that it preserves both anatomical structure and signal-to-noise characteristics even when the lesions are neighbouring grey matter and cerebrospinal fluid, and avoids excess blurring or rasterisation due to the choice of segmentation plane, and lesion shape, size and/or position.