Some people have reported relief from Lichen Sclerosus symptoms by using a homeopathy remedy called Pleo San Pseu 6X , a homeopathic remedy in drop form derived from Pseudomonas Aeruginosa. Pseudomonas Aeruginosa is widespread in nature, inhabiting soil, water, plants, and intestines of animals and humans, and it can cause infections, especially in patients with compromised immune systems. If you are familiar with homeopathy, the idea is that you treat with minute, highly diluted, doses of natural substances that in larger quantities would produce symptoms of illness even in healthy people.
Pleo San Pseu has been used for temporary relief of itching and congestion associated with allergies, including infectious and allergic dermatitis and pruritus (itching skin). It has also been used to treat burns, insect bites, angioneurotic edema, bronchial asthma, sinusitis, pharyngitis, chronic bronchitis, hay-fever, ear infections, and autoimmune diseases.
Apparently it can also be helpful in relieving itching related to Lichen Sclerosus in some patients. So if you know of a homeopath, it could be something worth discussing with them. Never self treat with homeopathic remedies even though they are easily available.