As always, I (GP) will try and address first the most likely reason for your search - Herpes? The reason you'll find L-Lysine mentioned amongst text of the Herpes Virus is that L-Lysine is the antagonist of L-Arginine, which nourishes the virus. More a reason why not to supplement L-Arginine though, than to supplement L-Lysine.
Another instance for your search is that the aforementioned L-Arginine, coupled with a pyroglutamate molecule (making Arginine pyroglutamate), is used in conjunction with L-Lysine as a reasonably common supplement aimed to stimulate growth hormone. Do not expect miracles though!
Other points of possible interest, L-Lysine (acting alongside L-Proline and Vitamin C) inhibits vascular lesions caused by Atherosclerosis. Also, collagen in the skin contains hydroxylysine and hydroxyproline - formed from L-Lysine and L-Proline.
Contraindications: Breast feeding, high cholesterol, liver or kidney problems, pregnancy.
Food sources include: Meat, Dairy Products, Eggs, Lima Beans, Brewers Yeast.