I just bought a Gibson Les Paul Custom Lite myself. Although it lacks a bit of the real low end and depth you get from a full thickness Les Paul, I thought it sounded very resonant myself with some great controlled bass with more sparkle on top. Sort of a halfway between a Les Paul and bolt-on neck Strat style.
I put in the Holy Divers for what I play (mostly metal although they do hard rock just fine), and they sound freakin' amazing in this guitar. I wasn't too happy with that pickup in previous superstrats that I tried, but in this guitar it just shines and I think it's the perfect guitar for the Diver's EQ curve, whereas a big thick Les Paul would be too thick and muddy, and a superstat not enough ooomph (from my experience).
Otherwise I would also recommend the Black Dog. I have it in a Les Paul Traditional that was a little thin/plinky on top for single notes in the high range, and this pickup thickened it right up. So I think it would work too. It's much more grindy and deeper sounding than the Holy Diver, and of course being lower output in the hot PAF range, but it takes crazy gain and I can imagine it would sound excellent in the Custom Lite as well.