The latter would be challenging if your focus is specifically on investigating the nature of the lesions themselves; but certainly not impossible. However, if you’re just looking to perform fixel-based analysis in the presence of lesions (be they in different locations across subjects or not; but realistically they are for a lot of pathologies), there’s no real problem at all. Depending on the kinds of lesions you’re talking about (and hence, the population you’re investigating), the WM component (“apparent fibre density”) may still work very well, and still tell you a lot about what happened to the actual white matter (i.e. axons). As @rsmith hinted at, there may also be information in the relative tissue intensities from multi-tissue CSD; but no worries @Marc , I’ve got an accepted ISMRM abstract exactly on that topic. I’ll make it available as soon as the ISMRM proceedings themselves are available (which should be pretty soon now). 
But in any way, @Marc, it would be helpful if you’d specify what kind of lesions you’re talking about (or which population). Are you talking about white matter hyperintensities (of the kind that would show brightly on a FLAIR)?