I suppose I've always gone for overdrive pedals with fairly smooth clipping (especially through Fender amps) but I get the impression to really get the best out of the LSIII you need to have the bright switch on, volume fairly high, gain/emphasis halfway or less and work the guitar volume (and boot it up the arse with a boost for Neil-esque fuzz-out.)
With the bright switch off I find you have to have the emphasis (tone) most of the way up otherwise it sounds a bit muted.
I suppose this pedal dials in a bit differently to the TS and Rat derivatives I otherwise use.