@OP. Sorry to be of only limited help as I haven't heard the Lumin. However, I have yet to hear any digital device with an integrated volume control that sounded better than the same device being run through a preamp of sufficient quality. It's something you need to audition for yourself though because it is device specific. However, in general, I've found the preamp option to be more relaxing to listen to and yet with better dynamics. Caveat again that the LeedH volume control in the Lumin is something I haven't heard. Quality of the volume control aside, however, it also depends on how good the analogue part of the output stage in the Lumin is versus the quality of the electronics in the pre. Bottom line - one needs to listen and decide.
A final PS. There is also the opportunity cost question - for example, how would the preamp compare to (if you don't have it) adding the X1 PSU to your S1.