It may help with symptoms, but no studies have been done for transmission. If you are looking to reduce transmission to partners, the only known ways to reduce that are to use antivirals (Valtrex, acyclovir, famvir) and condoms, along with avoiding sexual activity when you have any symptoms.
If you are looking to reduce outbreaks, studies are mixed for this.
Here's a very small study that showed promise - https://www.ncbi.nlm.nih.gov/pubmed/3115841
Here's one that showed a reduction in recurrences, but not in healing time - https://www.ncbi.nlm.nih.gov/pubmed/6153847
Lysine can have negative effects on your liver, kidneys, gall bladder and cholesterol. Talk to your doctor before starting it, especially since you would be taking it at high doses.