Users may (reasonably) cast LSJIMP as a multiple separation algorithm. LSJIMP outputs a multiple-free estimate of the primaries, which have been enhanced by the inversion. Conventionally, such multiple-free data is a prerequisite to velocity model building and depth migration. Stacking velocities, on the other hand, are available almost at the beginning of the processing flow, so in these situations, users may prefer to use imaging techniques which are less sensitive to velocity, like any method which uses stacking velocity instead of interval velocity.
One important point to emphasize is this: LSJIMP is an inversion algorithm which operates in an image space, not simply an imaging technique or a multiple separation technique. There are many choices of image space, but the central premises and potential of the LSJIMP method remain strong, regardless of the choice.