Hello,
Welcome to ehealthforum and thanks for writing
Valtrex is Valacyclovir and is commonly used for treating Herpetic infection.Though Valtrex has interaction with most of the drugs and can cause side effects but regarding the Lysine there has not been any study which might prove it.
L Lysine is a supplement and has not been approved by FDA which indicates that the effects are unknown so it is better to use any drug/supplement under your treating Physician's guidance.It is difficult to comment without a detailed history,disease,treatment duration,severity and extent of disease and a proper examination.
Kindly visit your Physician for evaluation and guidance.
Take care!