Every martial and melee art that targets inner organs don't have defense for lefties, both categories get same training
So no, left-handed takes shield either in left hand or takes 2 weapons
I don't think you could be more wrong if you tried.
I'm left handed, I do martial arts, both Asian unarmed and European longsword, and I ALWAYS fight left handed. If I tried to wield a sword in my right hand I'd die immediately. I also employ a mirrored base stance for karate, which actually works well when sparring cause few people know how to fight a lefty. It gives me an advantage as I'm used to fighting righties.
So, regardless of where your heart sits (which is pretty much center chest), you fight with your dominant hand. And it still makes sense to use a shield. You don't use a shield just to protect your heart, but to protect your entire body.