Final answer:
Alkaptonuria is a genetic condition that prevents proper metabolism of phenylalanine and tyrosine, potentially causing white lesions that do not rub off, among other symptoms such as darkened skin and joint damage.
Step-by-step explanation:
A metabolic disease that causes a white lesion that does not rub off may be indicative of several conditions. However, one relevant condition is alkaptonuria, a recessive genetic disease where individuals cannot metabolize two amino acids, phenylalanine and tyrosine, effectively.
This can lead to symptoms such as darkened skin and brown urine, and potentially cause joint damage and other complications. Similarly, other conditions that involve lesions or pigment changes in the skin due to metabolic issues include tyrosinosis, which leads to dark urine and 'ochronosis' marked by dark pigment deposition, as well as albinism, where there is a deficiency in melanin production due to a lack of tyrosinase enzyme. Conditions like xeroderma pigmentosa, which involve sensitivity to UV light and skin lesions, and Kaposi's sarcoma, a rare skin cancer in immunocompromised patients, while not metabolic diseases, also present with notable skin symptoms.