L-lysine is an amino acid that does only good.. you can take 4,000iu or mg(?) every morning and evening to fight a virus and for a miriad of other reasons. I'm not a professional but I would imagine it would only do your baby good. Quickly skimming the article that was posted by the last response looked like it verified this by giving doses for babies.. I think your baby will be quite protected from your healthy milk full of lysine:)