The only south paw I spar is a kid from my gym and I have sparred with him 100 + times.. When he gets tired and throws a lazy jab, I put my lead leg outside of him lead leg, lunge in a bit and my right hand to be body followed by left hook to his head. He falls for it every single time.. Always move to your left.. + whatever strategy you work it out, all those are applicable for your opponent as well. Better to keep that in mind as well.
use your left hand to neutralize his jab and get your lead foot outside his lead foot. You will be in the perfect position to land straight rights... Also remember the left hook to the body as south paw's liver are very close to your lead hook.
Move to your right and throw your left hook every time he throws his straight left. Or get under his left and work his body with right uppercuts.