Hi,
Welcome to the ehealthforum. I am glad to help you out.
There are no reported interactions between L-lysine and Vlatrex and you can take them together. But you should take both these drugs under medical supervision as they are not without side effects.
It is very difficult to precisely confirm a diagnosis without examination and investigations, and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care.