That makes no sense, Lysine competes with Arginine and depletes it. The main benefit of Lysine is to decrease nitric oxide levels, which Arginine produce.
BTW, @sladerunner69 and others, I'd be cautious with supplementing Lysine because it converts to carnitine, a known anti-thyroid and also the cause of cardiovascular disease from red meat consumption. Haidut mentions that lysine is also positively correlated with cardiovascular diseases in a study, which makes sense because of the carnitine connection. In general lowering nitric oxide will do your hair a lot of good, but like I wrote zinc and magnesium also do that. Those two would be safer, I don't think you'd get additional benefits from lysine except if you have taken arginine supps in the past.
@Elephanto, thanks. I'm definitely into the "first do no harm" principle, which is why I keep debating whether or not to supplement at all. What do you reckon is a safe amount of zinc? I've been using magnesium oil topically, but I dislike the oily feeling and it's hard to remove with ACV and baking soda.