My name is***** am sorry to hear that your dog has allergies.
L-lysine is an amino acid that is common in all meat and plant protein sources. It is an essential amino acid and excess is processed by the kidneys and excreted. Supplementing a dog with this amino acid is safe and should not cause any problems.
I have not heard of using lysine to treat skin conditions in dogs, but that does not mean that it cannot help. There are more and more reports of unusual ingredients helping dermatitis conditions in all species.
Others that I have heard of helping are flax seed oil, fish oil, and vitamin C and E supplements.
You can also try a fish and potato based diet as this addresses the omega fatty acid requirement as well as eliminating common food allergies such as beef, wheat, dairy, chicken and rice.
Best of luck to you and your dog!
I hope this answer helps you. Feel free to contact me if you have any further questions.
Kansas State University
College of Veterinary Medicine Class of 2001