When I spar south paws I like to parry with my leading hand and then counter off of that with a jab. you should do them same to orthodox fighters. Parry with your left and you're likely to get a right hand in the chops! :P

It's not the same as when two orthodox fighters fight, if we parry a left hand with our left then we're opening our self up... also if we parry and counter with the right... no chance! :P but when a southpaw and an Orthodox fighter fight it's like a mirror.... you can parry and counter off the same lead hand.