My dad, father in law, wife, and sister all shoot left handed. My dad and my wife prefer lever guns, but they don't have any blind brand loyalty. They shoot what they like, chambered for rounds that do the job at hand.
That being said, I wouldn't give a lever gun to a lefty-shooting child. If there is a case rupture, or other unpleasant event, the hot gas, bits of brass, and possibly bits of gun, will blow right into a left hander's face, via the ejection port and loading gate. When lever guns come apart, regardless of cause, anything to the right of the receiver is in trouble. If a knowledgeable adult wants to shoot one anyway, fine, but I wouldn't hand one to a kid. If that one-in-a-million malfunction did occur, and my child was injured, I'd have a hard time looking myself in the mirror.
My son favors his left hand, so this topic may come up in his future. Even though his name is Henry, after the lever gun, even though my handle is leverfan, even though I started shooting and hunting with lever action rifles, Henry isn't going to shoot one if he turns out to be a lefty. If he still wants one when he's older, and understands the risks, that's fine. Until then, he'll get single shots that open and eject to the top, or left handed bolt guns. Savage makes fine, affordable lefty bolt guns in short action calibers, perfect for a young shooter. There's a brand new, unfired 7mm-08 waiting in my safe, with a bolt hanging off the left side of the action, just in case.