Actually, L-lysine is an essential amino acid (one our bodies don't produce, and we must get it from dietary sources) and is therefore a nutritional therapy, not a homeopathic remedy.
Homeopathy is a medical discipline based on a "holistic" (entire body, not just each individual part) approach, and using highly diluted remedies. I don't quite understand the whole thing. I've read some good explanations, and I know enough people who swear by it to believe that it works, but I can't explain it any better than that LOL!
If you really want to knock out a herpes outbreak, it helps to load up on foods that contain l-Lysine such as milk/cheese, eggs, meat, poultry, fish, beans, potatoes. Avoid foods containing lots of L-arginine such as nuts, seeds, grains, peanuts and chocolate. This is the advice that was in a book my parents had called "Let's Play Doctor" about treating yourself with diet and nutrition, and it worked very well for me. I have noticed sometimes when I was tired and run down, and had eaten more nuts and chocolate than usual, I would sometimes get that tingly feeling on my lip... and know I needed to up my lysine intake and cut back on the chocolate!