I play both humbuckers and singles through my LSS. When playing a LP straight into the LSS, you will have a tone much like Dicky Betts with the Allman Bros. (I keep the "thickness"switch in the UP position, it tends to give a bit of a British spank to your sound) When I am going for a classic rock overdrive sound (Jeff Beck, Joe Walsh, Led Zepp etc) with Les Pauls and other humbuckers, I have a Rob Keeley Rat pedal that just ooooozes classic distortion tone through this amp w/ the pedal level (volume) around 1:00 and the distortion only at 10:00....it is pretty sweet. Also the Keeley Rat has 2 extra modes toggled in w/ a 3-way mini toggle that make for nice pallot of other tones. In one mode, you get the classic RAT, in another it is like a mellowed out classic RAT sound with a bit of a boost in the bass; the other mode is a clean boost.
The Keeley Rat is my "go-to" pedal for all of my EL-34 and EL-84 amps when I want to make a humbucker sound classic; in fact, if you do a search of RAT pedal artists, or go to their website, you will see that not only the ones mentioned above use it, (and used it in the 70's) but tons more did too. Get the guitar, but get this pedal!!!